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DOE OSTI2021

Integration of the Back End of the Nuclear Fuel Cycle

Management of spent nuclear fuel and high-level radioactive waste consists of three main phases – storage, transportation, and disposal – commonly referred to as the back end of the nuclear fuel cycle. Current practice for commercial spent nuclear fuel management in the United States (US) includes temporary storage of spent fuel in both pools and dry storage systems at operating or shutdown nuclear power plants. Storage pools are filling to their operational capacity, and management of the approximately 2,200 metric tons of spent fuel newly discharged each year requires transferring older and cooler spent fuel from pools into dry storage. Unless a repository becomes available that can accept spent fuel for permanent disposal, projections indicate that the US will have approximately 136,000 metric tons of spent fuel in dry storage systems by mid-century, when the last plants in the current reactor fleet are decommissioned. Current designs for dry storage systems rely on large multi-assembly canisters, the most common of which are so-called “dual-purpose canisters” (DPCs). DPCs are certified for both storage and transportation, but are not designed or licensed for permanent disposal. The large capacity (greater number of spent fuel assemblies) of these canisters can lead to higher canister temperatures, which can delay transportation and/or complicate disposal. This current management practice, in which the utilities continue loading an ever-increasing inventory of larger DPCs, does not emphasize integration among storage, transportation, and disposal. This lack of integration does not cause safety issues, but it does lead to a suboptimal system that increases costs, complicates storage and transportation operations, and limits options for permanent disposal. This paper describes strategies for improving integration of management practices in the US across the entire back end of the nuclear fuel cycle. The complex interactions between storage, transportation, and disposal make a single optimal solution unlikely. However, efforts to integrate various phases of nuclear waste management can have the greatest impact if they begin promptly and continue to evolve throughout the remaining life of the current fuel cycle. A key factor that influences the path forward for integration of nuclear waste management practices is the identification of the timing and location for a repository. The most cost-effective path forward would be to open a repository by mid-century with the capability to directly dispose of DPCs without repackaging the spent fuel into disposalready canisters. Options that involve repackaging of spent fuel from DPCs into disposalready canisters or that delay the repository opening significantly beyond mid-century could add 10s of billions of dollars to the total system life cycle cost.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Bridging the Gap: User-Centric Energy Monitoring for Policy-Driven Application Optimization in HPC Data Centers

Application energy optimization in HPC data centers face two critical gaps. Systematic methodologies that connect data center policies to application decisions and accessible monitoring tools that enable data-driven optimization. We address both gaps through two complementary pillars. First, we present a methodology based on extended weighted Energy Delay Product (EDP) to translate data center operational priorities and integrate energy considerations into the energy optimization workflow which starts from continuous monitoring through targeted optimization. Second, we present a user-space monitoring tool, Omnistat, that enables this methodology by providing developers with direct access to actionable energy telemetry. Through deployment on the Frontier supercomputer and case studies exploring performance-energy trade-offs, we show how these pillars help energy as an integral optimization target for developers as active participants in data center efficiency.

Shin, Woong [ORNL] (ORCID:0000000172077814)↗

NASA NTRS2011

Carbon Nanofiber-Based, High-Frequency, High-Q, Miniaturized Mechanical Resonators

High Q resonators are a critical component of stable, low-noise communication systems, radar, and precise timing applications such as atomic clocks. In electronic resonators based on Si integrated circuits, resistive losses increase as a result of the continued reduction in device dimensions, which decreases their Q values. On the other hand, due to the mechanical construct of bulk acoustic wave (BAW) and surface acoustic wave (SAW) resonators, such loss mechanisms are absent, enabling higher Q-values for both BAW and SAW resonators compared to their electronic counterparts. The other advantages of mechanical resonators are their inherently higher radiation tolerance, a factor that makes them attractive for NASA s extreme environment planetary missions, for example to the Jovian environments where the radiation doses are at hostile levels. Despite these advantages, both BAW and SAW resonators suffer from low resonant frequencies and they are also physically large, which precludes their integration into miniaturized electronic systems. Because there is a need to move the resonant frequency of oscillators to the order of gigahertz, new technologies and materials are being investigated that will make performance at those frequencies attainable. By moving to nanoscale structures, in this case vertically oriented, cantilevered carbon nanotubes (CNTs), that have larger aspect ratios (length/thickness) and extremely high elastic moduli, it is possible to overcome the two disadvantages of both bulk acoustic wave (BAW) and surface acoustic wave (SAW) resonators. Nano-electro-mechanical systems (NEMS) that utilize high aspect ratio nanomaterials exhibiting high elastic moduli (e.g., carbon-based nanomaterials) benefit from high Qs, operate at high frequency, and have small force constants that translate to high responsivity that results in improved sensitivity, lower power consumption, and im - proved tunablity. NEMS resonators have recently been demonstrated using topdown, lithographically fabricated ap - proaches to form cantilever or bridgetype structures. Top-down approaches, however, rely on complicated and expensive e-beam lithography, and often require a release mechanism. Reso - nance effects in structures synthesized using bottom-up approaches have also recently been reported based on carbon nanotubes, but such approaches have relied on a planar two-dimensional (2D) geometry. In this innovation, vertically aligned tubes synthesized using a bottom- up approach have been considered, where the vertical orientation of the tubes has the potential to increase integration density even further. The simulation of a vertically oriented, cantilevered carbon nanotube was performed using COMSOL Multi - physics, a finite element simulation package. All simulations were performed in a 2D geometry that provided consistent results and minimized computational complexity. The simulations assumed a vertically oriented, cantilevered nanotube of uniform density (1.5 g/cu cm). An elastic modulus was assumed to be 600 GPa, relative permittivity of the nanotube was assumed to be 5.0, and Poisson s ratio was assumed to be 0.2. It should be noted that the relative permittivity and Poisson s ratio for the nanotubes of interest are not known accurately. However, as in previous simulations, the relative permittivity and Poisson s ratios were treated as weak variables in the simulation, and no significant changes were recognized when these variables were varied.

Kaul, Anupama B.↗

NASA NTRS1981

Integrated propulsion for near-Earth space missions. Volume 1: Executive summary

Tradeoffs between electric propulsion system mass ratio and transfer time from LEO to GEO were conducted parametrically for various thruster efficiency, specific impulse, and other propulsion parameters. A computer model was developed for performing orbit transfer calculations which included the effects of aerodynamic drag, radiation degradation, and occultation. The tradeoff results showed that thruster technology areas for integrated propulsion should be directed towards improving primary thruster efficiency in the range from 1500 to 2500 seconds, and be continued towards reducing specific mass. Comparison of auxiliary propulsion systems showed large total propellant mass savings with integrated electric auxiliary propulsion. Stationkeeping is the most demanding on orbit propulsion requirement. At area densities above 0.5 sq m/kg, East-West stationkeeping requirements from solar pressure exceed North-South stationkeeping requirements from gravitational forces. A solar array pointing strategy was developed to minimize the effects of atmospheric drag at low altitude, enabling electric propulsion to initiate orbit transfer at Shuttle's maximum cargo carrying altitude. Gravity gradient torques are used during ascent to sustain the spacecraft roll motion required for optimum solar array illumination. A near optimum cover glass thickness of 6 mils was established for LEO to GEO transfer.

Dailey, C. L.↗

NASA NTRS2015

Software Defined Radio Architecture Contributions to Next Generation Space Communications

Space communications architecture concepts, comprising the elements of the system, the interactions among them, and the principles that govern their development, are essential factors in developing National Aeronautics and Space Administration (NASA) future exploration and science missions. Accordingly, vital architectural attributes encompass flexibility, the extensibility to insert future capabilities, and to enable evolution to provide interoperability with other current and future systems. Space communications architectures and technologies for this century must satisfy a growing set of requirements, including those for Earth sensing, collaborative observation missions, robotic scientific missions, human missions for exploration of the Moon and Mars where surface activities require supporting communications, and in-space observatories for observing the earth, as well as other star systems and the universe. An advanced, integrated, communications infrastructure will enable the reliable, multipoint, high-data-rate capabilities needed on demand to provide continuous, maximum coverage for areas of concentrated activity. Importantly, the cost/value proposition of the future architecture must be an integral part of its design; an affordable and sustainable architecture is indispensable within anticipated future budget environments. Effective architecture design informs decision makers with insight into the capabilities needed to efficiently satisfy the demanding space-communication requirements of future missions and formulate appropriate requirements. A driving requirement for the architecture is the extensibility to address new requirements and provide low-cost on-ramps for new capabilities insertion, ensuring graceful growth as new functionality and new technologies are infused into the network infrastructure. In addition to extensibility, another key architectural attribute of the space communication equipment's interoperability with other NASA communications systems, as well as those communications and navigation systems operated by international space agencies and civilian and government agencies. In this paper, we review the philosophies, technologies, architectural attributes, mission services, and communications capabilities that form the structure of candidate next-generation integrated communication architectures for space communications and navigation. A key area that this paper explores is from the development and operation of the software defined radio for the NASA Space Communications and Navigation (SCaN) Testbed currently on the International Space Station (ISS). Evaluating the lessons learned from development and operation feed back into the communications architecture. Leveraging the reconfigurability provides a change in the way that operations are done and must be considered. Quantifying the impact on the NASA Space Telecommunications Radio System (STRS) software defined radio architecture provides feedback to keep the standard useful and up to date. NASA is not the only customer of these radios. Software defined radios are developed for other applications, and taking advantage of these developments promotes an architecture that is cost effective and sustainable. Developments in the following areas such as an updated operating environment, higher data rates, networking and security can be leveraged. The ability to sustain an architecture that uses radios for multiple markets can lower costs and keep new technology infused.

Lessons Learned↗

DOE OSTI2025

Scenario Generation for Built Environment Decision Support under Uncertainty: Case Studies of Airflow Modeling and Climate-Resilient Infrastructure System Design

When confronted with unforeseen challenges, practicing informed decision making is crucial for enhancing resilience in the built environment. While scan-to-building information modeling (BIM) is a well-established approach for creating detailed digital representations of physical assets, its application in assessing and improving infrastructure resilience remains underexplored. This study addresses this gap by proposing a novel application of scan-to-BIM, namely, scan-to-BIM-to-digital twin (S-BIM-DT) workflow. By integrating reality capture and digital twin technologies, this workflow creates continuously updated and accurate digital representations of physical assets, enabling the generation of various scenarios. Unlike traditional methods, the S BIM-DT workflow facilitates continuous model refinement, supporting informed resilience strategies. By combining these technologies into a cohesive process, the workflow facilitates decision making under uncertainty, enabling stakeholders to evaluate and respond to various scenarios effectively. We demonstrate the implementation of the S-BIM-DT workflow through two use cases that highlight its capability to enhance resilience at different scales. The first use case involves the Combined Transportation, Emergency, and Communications Center (CTECC) in Austin, Texas. BIM-enriched computational fluid dynamics (CFD) modeling simulates airflow and develops alternative scenarios for optimizing the heating, ventilation, and air conditioning (HVAC) systems. This approach enhances resilience against airborne health threats in a postCOVID context. The second use case focuses on designated areas within Beaumont, Texas, as part of the Southeast Texas Urban Integrated Field Laboratory (SETx-UIFL) research. By developing inundation maps to assess extreme weather events, this modeling aids in preparedness efforts and informs the development of climate-resilient infrastructure in vulnerable neighborhoods. Results indicate that the S-BIM-DT workflow effectively generates scenarios that enhance resilience in the built environment by facilitating informed decision making. Furthermore, this study serves as a bridge between advanced scan-to-BIM methodologies and the practical strategies needed to improve built infrastructure resilience.

Built environment↗

NASA NTRS1999

Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations that Arise from Nonlinear Two-Point Boundary Value Problems

In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + integral(0 to 1) g(x,t) F(t, y(t)) dt, 0 less than or equal to x less than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integrals equations arise, e.g., when one applies Green's function techniques to nonlinear two-point boundary value problems of the form U''(x) = f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and g(l) = y(sub 1), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trapezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.

Sidi, Avram↗

DOE OSTI2022

Lefschetz thimble quantum Monte Carlo for spin systems

Monte Carlo simulations are useful tools for modeling quantum systems, but in some cases they suffer from a sign problem, leading to an exponential slow down in their convergence to a value. While solving the sign problem is generically NP hard, many techniques exist for mitigating the sign problem in specific cases; in particular, the technique of deforming the Monte Carlo simulation's plane of integration onto Lefschetz thimbles (complex hypersurfaces of stationary phase) has seen significant success in the context of quantum field theories. We extend this methodology to spin systems by utilizing spin coherent state path integrals to reexpress the spin system's partition function in terms of continuous variables. Using some toy systems, we demonstrate its effectiveness at lessening the sign problem in this setting, despite the fact that the initial mapping to spin coherent states introduces its own sign problem. The standard formulation of the spin coherent path integral is known to make use of uncontrolled approximations; despite this, for large spins they are typically considered to yield accurate results, so it is somewhat surprising that our results show significant systematic errors. Furthermore, possibly of independent interest, our use of Lefschetz thimbles to overcome the intrinsic sign problem in spin coherent state path integral Monte Carlo enables a novel numerical demonstration of a breakdown in the spin coherent path integral.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2013

Simulations of Continuous Descent Operations with Arrival-management Automation and Mixed Flight-deck Interval Management Equipage

Air traffic management simulations conducted in the Airspace Operations Laboratory at NASA Ames Research Center have addressed the integration of trajectory-based arrival-management automation, controller tools, and Flight-Deck Interval Management avionics to enable Continuous Descent Operations (CDOs) during periods of sustained high traffic demand. The simulations are devoted to maturing the integrated system for field demonstration, and refining the controller tools, clearance phraseology, and procedures specified in the associated concept of operations. The results indicate a variety of factors impact the concept's safety and viability from a controller's perspective, including en-route preconditioning of arrival flows, useable clearance phraseology, and the characteristics of airspace, routes, and traffic-management methods in use at a particular site. Clear understanding of automation behavior and required shifts in roles and responsibilities is important for controller acceptance and realizing potential benefits. This paper discusses the simulations, drawing parallels with results from related European efforts. The most recent study found en-route controllers can effectively precondition arrival flows, which significantly improved route conformance during CDOs. Controllers found the tools acceptable, in line with previous studies.

arrival management↗

NASA NTRS1976

Monitoring estuarine circulation and ocean waste dispersion using an integrated satellite-aircraft-drogue approach

The mounting economic pressure to extract oil and other resources from the Continental Shelf and to continue using the Shelf for waste disposal is creating a need for cost-effective synoptic means of determining currents in this area. An integrated satellite-aircraft-drogue approach has been developed which employs remotely tracked expendable drogues together with satellite and aircraft observations of waste plumes and tracers, such as dyes or suspended sediment. Tests conducted on the Continental Shelf and in Delaware Bay indicate that the system provides a cost-effective means of studying current circulation, oil slick movement, and ocean waste dispersion even under severe environmental conditions.

Klemas, V.↗

DOE OSTI2021

Microfluidic Liquid-Liquid Extraction Chip with Integrated Raman Sensors (Phase I and Phase II Final Report)

As demand for electricity continues to increase worldwide, the world’s nuclear power generating capacity will continue to grow. Nuclear power is the most environmentally benign way of producing electricity on a large scale. The long-term successful use of nuclear power, however, is critically dependent upon adequate and safe processing and disposal of spent nuclear fuels. A very important feature of nuclear energy is that spent fuels can be reprocessed to recover fissile and fertile materials that can then be used as fresh fuel for nuclear power plants. The DOE-NE Fuel Cycle Research and Development (FCR&D) is currently developing nuclear material reprocessing technologies. In a typical nuclear fuel reprocessing system, centrifugal contactors are used as liquid-liquid extraction devices where two immiscible liquids are mixed at high speeds using a rotor, which creates a fine dispersion of droplets of organic phase in an aqueous phase that contains the analyte. Understanding the extraction efficiency at these contactors through modeling and simulation is important in the development of reprocessing technologies and the optimization of current technologies such as the PUREX process. The outcome of this program will be a liquid-liquid microfluidic flow cell chip with embedded spectroscopic sensors for the analysis of extracted analytes. This device will be useful in the optimization of new fuel reprocessing schemes as well as existing reprocessing processes by providing a microfluidic modeling platform to optimize extraction parameters. The Phase I and Phase II work developed a microfluidic chip design that allows integration of Raman and absorption fiber optic probes and successfully demonstrated the feasibility of using Raman and absorption probes to detect key analytes that partition into the aqueous and organic phases.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NASA NTRS1991

Rotordynamic Instability Problems in High-Performance Turbomachinery, 1990

The present workshop continues to report field experience and experimental results, and it expands the use of computational and control techniques with the integration of damper, bearing, and eccentric seal operation results. The intent of the workshop was to provide a continuing impetus for an understanding and resolution of these problems.

Source record↗

NASA NTRS2012

Lessons Learned during Thermal Hardware Integration on the Global Precipitation Measurement Satellite

The Global Precipitation Measurement mission is a joint NASA/JAXA mission scheduled for launch in late 2013. The integration of thermal hardware onto the satellite began in the Fall of 2010 and will continue through the Summer of 2012. The thermal hardware on the mission included several constant conductance heat pipes, heaters, thermostats, thermocouples radiator coatings and blankets. During integration several problems arose and insights were gained that would help future satellite integrations. Also lessons learned from previous missions were implemented with varying degrees of success. These insights can be arranged into three categories. 1) the specification of flight hardware using analysis results and the available mechanical resources. 2) The integration of thermal flight hardware onto the spacecraft, 3) The preparation and implementation of testing the thermal flight via touch tests, resistance measurements and thermal vacuum testing.

Cottingham, Christine↗

NASA NTRS1992

1992 NASA Life Support Systems Analysis workshop

The 1992 Life Support Systems Analysis Workshop was sponsored by NASA's Office of Aeronautics and Space Technology (OAST) to integrate the inputs from, disseminate information to, and foster communication among NASA, industry, and academic specialists. The workshop continued discussion and definition of key issues identified in the 1991 workshop, including: (1) modeling and experimental validation; (2) definition of systems analysis evaluation criteria; (3) integration of modeling at multiple levels; and (4) assessment of process control modeling approaches. Through both the 1991 and 1992 workshops, NASA has continued to seek input from industry and university chemical process modeling and analysis experts, and to introduce and apply new systems analysis approaches to life support systems. The workshop included technical presentations, discussions, and interactive planning, with sufficient time allocated for discussion of both technology status and technology development recommendations. Key personnel currently involved with life support technology developments from NASA, industry, and academia provided input to the status and priorities of current and future systems analysis methods and requirements.

Evanich, Peggy L.↗

NASA NTRS2019

Hybrid Transportation System Integrated Trajectory Design and Optimization for Mars Landing Site Accessibility

NASA’s Mars Study Capability Team continues the agency’s efforts to study and refine the nation’s plan to field a sustainable human Mars campaign. One of the primary open issues left unanswered during previous analysis cycles was the uncertainty of the impact to the vehicle performance requirement to deliver crew and cargo to the same landing site across multiple mission opportunities. The Mars Study Capability Team has recently developed an integrated trajectory optimization and system closure model to solve the complex interplanetary trajectory optimization using both low-thrust and high-thrust maneuvers. This paper demonstrates the capability of this new integrated trajectory design and optimization method as it applies to the landing site accessibility problem for the Hybrid transportation architecture. The results showed that the current vehicle is capable of reaching up to +20 degree latitude and down to -20 degree latitude in every mission opportunity from 2033 to 2052. However, reaching latitudes beyond +/- 20 required more propellant than the spacecraft is currently designed to carry for many of the mission opportunities.

Chai, Patrick R.↗

NASA NTRS2002

ARIES: NASA Langley's Airborne Research Facility

In 1994, the NASA Langley Research Center (LaRC) acquired a B-757-200 aircraft to replace the aging B-737 Transport Systems Research Vehicle (TSRV). The TSRV was a modified B-737-100, which served as a trailblazer in the development of glass cockpit technologies and other innovative aeronautical concepts. The mission for the B-757 is to continue the three-decade tradition of civil transport technology research begun by the TSRV. Since its arrival at Langley, this standard 757 aircraft has undergone extensive modifications to transform it into an aeronautical research "flying laboratory". With this transformation, the aircraft, which has been designated Airborne Research Integrated Experiments System (ARIES), has become a unique national asset which will continue to benefit the U.S. aviation industry and commercial airline customers for many generations to come. This paper will discuss the evolution of the modifications, detail the current capabilities of the research systems, and provide an overview of the research contributions already achieved.

Wusk, Michael S.↗

NASA NTRS2010

Using Leaf Chlorophyll to Parameterize Light-Use-Efficiency Within a Thermal-Based Carbon, Water and Energy Exchange Model

Chlorophylls absorb photosynthetically active radiation and thus function as vital pigments for photosynthesis, which makes leaf chlorophyll content (C(sub ab) useful for monitoring vegetation productivity and an important indicator of the overall plant physiological condition. This study investigates the utility of integrating remotely sensed estimates of C(sub ab) into a thermal-based Two-Source Energy Balance (TSEB) model that estimates land-surface CO2 and energy fluxes using an analytical, light-use-efficiency (LUE) based model of canopy resistance. The LUE model component computes canopy-scale carbon assimilation and transpiration fluxes and incorporates LUE modifications from a nominal (species-dependent) value (LUE(sub n)) in response to short term variations in environmental conditions, However LUE(sub n) may need adjustment on a daily timescale to accommodate changes in plant phenology, physiological condition and nutrient status. Day to day variations in LUE(sub n) were assessed for a heterogeneous corn crop field in Maryland, U,S.A. through model calibration with eddy covariance CO2 flux tower observations. The optimized daily LUE(sub n) values were then compared to estimates of C(sub ab) integrated from gridded maps of chlorophyll content weighted over the tower flux source area. The time continuous maps of daily C(sub ab) over the study field were generated by focusing in-situ measurements with retrievals generated with an integrated radiative transfer modeling tool (accurate to within +/-10%) using at-sensor radiances in green, red and near-infrared wavelengths acquired with an aircraft imaging system. The resultant daily changes in C(sub ab) within the tower flux source area generally correlated well with corresponding changes in daily calibrated LUE(sub n) derived from the tower flux data, and hourly water, energy and carbon flux estimation accuracies from TSEB were significantly improved when using C(sub ab) for delineating spatio-temporal variations in LUE(sub n). The results demonstrate the synergy between thermal infrared and shortwave reflective wavebands in producing valuable remote sensing data for operational monitoring of carbon and water fluxes.

Houlborg, Rasmus↗

NASA NTRS1999

Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations That Arise from Nonlinear Two-Point Boundary Value Problems

In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + definite integral of g(x, t)F(t,y(t))dt with limits between 0 and 1,0 less than or equal to x les than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integral equations arise, e.g., when one applied Green's function techniques to nonlinear two-point boundary value problems of the form y "(x) =f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and y(l) = y(sub l), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trepezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal rule, thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.

Sidi, Avram↗