An Encke-type special perturbation method.
Encke type analytical-numerical integration for solving differential equations of modified set of Lagrange planetary equations, obtaining satellite ephemeris for orbit prediction
Born, G. H.↗
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Numerical solution of Tricomi equation using theory of symmetric positive differential equations.
Boundary conditions for Tricomi equation in symmetric positive form, showing analytical and finite difference solutions
Katsanis, T.↗
Numerical predictions for circular tube laminarization by heating.
Numerical program solving partial differential equations parabolic system for internal turbulent gas flow extended to flows undergoing circular tube laminarization by heating
Bankston, C. A.↗
Pseudo-Runge-Kutta methods of the fifth order
Fifth-order pseudo-Runge-Kutta methods for numerical solution of ordinary differential equations, determining optimal parameters
Gruttke, W. B.↗
An integrator design
Integrator design to provide subroutines for numerical solution of ordinary differential equations
Krogh, F. T.↗
The initial development of the general non-isoenergetic compressible free shear layer
Numerical solution of partial differential equations governing intial development of general nonisoenergetic compressible free shear layer
Carpenter, P.↗
IBM system/360 assembly language interval arithmetic software
Computer software designed to perform interval arithmetic is described. An interval is defined as the set of all real numbers between two given numbers including or excluding one or both endpoints. Interval arithmetic consists of the various elementary arithmetic operations defined on the set of all intervals, such as interval addition, subtraction, union, etc. One of the main applications of interval arithmetic is in the area of error analysis of computer calculations. For example, it has been used sucessfully to compute bounds on sounding errors in the solution of linear algebraic systems, error bounds in numerical solutions of ordinary differential equations, as well as integral equations and boundary value problems. The described software enables users to implement algorithms of the type described in references efficiently on the IBM 360 system.
Phillips, E. J.↗
Orbit improvement from satellite imaging data obtainable from the Mariner/Jupiter/Saturn 1977 missions
Equations of motion are established for a dynamic system in which a spacecraft flies close to and interacts with an outer planet and one or more of its satellites. For the computation of the state and mass partials needed in the orbit corrections, a set of variational equations is derived. These assume a notably compact form through the introduction of a matrix operator D. The above system of differential equations is integrated numerically on a computer.
Aksnes, K.↗
Conductivity of a two-dimensional guiding center plasma.
The Kubo method is used to calculate the electrical conductivity of a two-dimensional, strongly magnetized plasma. The particles interact through (logarithmic) electrostatic potentials and move with their guiding center drift velocities (Taylor-McNamara model). The thermal equilibrium dc conductivity can be evaluated analytically, but the ac conductivity involves numerical solution of a differential equation. Both conductivities fall off as the inverse first power of the magnetic field strength.
Montgomery, D.↗
Simplified analysis and optimization of space base and space shuttle heat rejection systems
A simplified radiator system analysis was performed to predict steady state radiator system performance. The system performance was found to be describable in terms of five non-dimensional system parameters. The governing differential equations are integrated numerically to yield the enthalpy rejection for the coolant fluid. The simplified analysis was extended to produce the derivatives of the coolant exit temperature with respect to the governing system parameters. A procedure was developed to find the optimum set of system parameters which yields the lowest possible coolant exit temperature for either a given projected area or a given total mass. The process can be inverted to yield either the minimum area or the minimum mass, together with the optimum geometry, for a specified heat rejection rate.
Wulff, W.↗
Vertical distribution of vibrational energy of molecular nitrogen in a stable auroral red arc and its effect on ionospheric electron densities
Previous solutions of the problem of the distribution of vibrationally excited molecular nitrogen in the thermosphere have either assumed a Boltzmann distribution and considered diffusion as one of the loss processes or solved for the energy level populations and neglected diffusion. Both of the previous approaches are combined by solving the time dependent continuity equations, including the diffusion process, for the first six energy levels of molecular nitrogen for conditions in the thermosphere corresponding to a stable auroral red arc. The primary source of molecular nitrogen excitation was subexcitation, and inelastic collisions between thermal electrons and molecular nitrogen. The reaction rates for this process were calculated from published cross section calculations. The loss processes for vibrational energy were electron and atomic oxygen quenching and vibrational energy exchange. The coupled sets of nonlinear, partial differential equations were solved numerically by employing finite difference equations.
Newton, G. P.↗
Prior-to-failure extension of flaws under monotonic and pulsating loadings.
An equation governing the prior-to-failure crack propagation is proposed. For a rate-sensitive solid containing a two-dimensional crack and subject to the tensile mode of fracture the differential equations are integrated numerically for loads increasing monotonically in time. The resulting integral curves of load vs crack length and length vs time indicate that the growth of cracks in the subcritical range is strongly rate-dependent. The fatigue growth, viewed as a sequence of slow growth periods, is simulated on an EAI 380 analog computer. The fourth-power law proposed by Paris is confirmed only within certain range of high-cycle fatigue propagation and for a rate-insensitive solid. Otherwise, i.e., for a more pronounced rate dependence induced by viscosity of a solid and/or in the proximity of the final instability point, the growth is markedly enhanced.
Wnuk, M. P.↗
Orbit improvement from satellite imaging data obtainable from outer planet missions.
Equations of motion are established for a dynamical system in which a spacecraft flies close to and interacts with an outer planet and one or more of its satellites. For the computation of the state and mass partials needed in a simultaneous orbit correction of n interacting bodies, a notably compact set of variational equations is derived. The above system of differential equations is integrated numerically on a computer. Spacecraft-satellite direction measurements accurate to plus or minus 10 sec were simulated along three representative trajectories (Mariner/Jupiter/Saturn 1977 missions) approaching Io, Titan, and Iapetus to within 41000, 13000, and 7000 km, respectively. The paper concludes with a brief discussion of the need for future work on the orbits of the satellites of the outer planets.
Aksnes, K.↗
Prior-to-failure extension of flaws under monotonic and pulsating loadings: Inelastic fatigue
An equation governing the prior to failure crack propagation is proposed. For a rate-sensitive solid containing two-dimensional crack and subject to the tensile mode of fracture, the differential equations are integrated numerically for the loads increasing monotonically in time. The resulting integral curves sigma = sigma(l) and l = l(t), i.e. load vs. crack length and length vs. time, indicate that the growth of cracks in the subcritical range is strongly rate dependent. The fatigue growth, viewed as a sequence of slow growth periods, is simulated on an EAI 380 analogue computer. The fourth power law proposed by Paris is confirmed only within a certain range of high-cycle fatigue propagation and for a rate-insensitive solid. For a more pronounced rate dependency, induced by the viscosity of a solid and/or in the proximity of the final instability point, the growth is markedly enhanced.
Wnuk, M. P.↗
Some procedures for computerized electronic data processing of absorption measurements from artificial earth satellites
The processing of data obtained from solar absorption radiation measurements is discussed. The position of the satellite was obtained by numerical integration of the differential equations of motion using initial conditions. The position of the sun was calculated as a function of time, and the tangential elevation was determined approximately from the positions of the satellite and the sun. The coefficients of an approximation formula and of a data smoothing process were determined, and the inversion of an Abel integral equation is solved analytically.
Trinkkeller, B.↗
Historical evolution of vortex-lattice methods
A review of the beginning and some orientation of the vortex-lattice method were given. The historical course of this method was followed in conjunction with its field of computational fluid dynamics, spanning the period from L.F. Richardson's paper in 1910 to 1975. The following landmarks were pointed out: numerical analysis of partial differential equations, lifting-line theory, finite-difference method, 1/4-3/4 rule, block relaxation technique, application of electronic computers, and advanced panel methods.
Deyoung, J.↗
A formulation consideration for orthogonal collocation procedures
Numerical instabilities often arise in the use of high-ordered collocation approximations for numerically solving parabolic partial differential equations. These problems may be reduced by formulations involving evaluation of collocation polynomials rather than combination of the polynomials into a power series. As an illustration, two formulations using shifted Legendre polynomials of order 26 and less are compared.
Lashmet, P. K.↗
A three-dimensional, time-dependent model of Mobile Bay
A three-dimensional, time-variant mathematical model for momentum and mass transport in estuaries was developed and its solution implemented on a digital computer. The mathematical model is based on state and conservation equations applied to turbulent flow of a two-component, incompressible fluid having a free surface. Thus, bouyancy effects caused by density differences between the fresh and salt water, inertia from thare river and tidal currents, and differences in hydrostatic head are taken into account. The conservation equations, which are partial differential equations, are solved numerically by an explicit, one-step finite difference scheme and the solutions displayed numerically and graphically. To test the validity of the model, a specific estuary for which scaled model and experimental field data are available, Mobile Bay, was simulated. Comparisons of velocity, salinity and water level data show that the model is valid and a viable means of simulating the hydrodynamics and mass transport in non-idealized estuaries.
Pitts, F. H.↗