SEARCH · Engineering Papers
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Numerical integration based on definition of Riemann integral, describing application to nonlinear integral equations of isotropic scattering of radiation in plane parallel atmosphere
Numerical integration methods for the solution of initial value problems for ordinary vector differential equations may be modelled as discrete time feedback systems. The stability criteria discovered in modern control theory are applied to these systems and criteria involving the routine, the step size and the differential equation are derived. Linear multistep, Runge-Kutta, and predictor-corrector methods are all investigated.
We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches, one obtains an exponential speed increase in comparison to the fastest known classical deterministic algotithms and a quadratic speed increase incomparison to classical Monte Carlo methods.
Self-starting multistep methods for numerical integration of ordinary differential equations
Accumulation of errors using numerical integration methods for solving celestial equations of motion
Operational unification of finite difference methods for numerical integration of ordinary differential equations
Predictor-corrector algorithm applicable to numerical integration of satellite orbits in multirevolution steps
Numerical integration methods for computing flow of gas in chemical nonequilibrium behind normal shock wave
Cowell numerical integration and satellite orbit calculation
Numerical integration orbits and Brouwer and modified Brouwer orbits
Algorithm for use in estimating accumulated numerical integration errors
Digital simulation for error analysis of numerical integration schemes
Error growth and stability analyzed for numerical integration of differential equations in chemical kinetics
We present our experience in porting optimized CUDA implementations to oneAPI. We focus on the use case of numerical integration, particularly the CUDA implementations of PAGANI and $m$-Cubes. We faced several challenges that caused performance degradation in the oneAPI ports. These include differences in utilized registers per thread, compiler optimizations, and mappings of CUDA library calls to oneAPI equivalents. After addressing those challenges, we tested both the PAGANI and m-Cubes integrators on numerous integrands of various characteristics. To evaluate the quality of the ports, we collected performance metrics of the CUDA and oneAPI implementations on the Nvidia V100 GPU. We found that the oneAPI ports often achieve comparable performance to the CUDA versions, and that they are at most 10% slower.
Numerical integration of coupled first order ODE OF greatly differing time constant
A comparison theorem estimating the difference between solutions of a perturbed and unperturbed equation is obtained. This is then applied to obtain error estimates in numerical integration problems, in particular, those problems involving computation of satellite orbits. The main result is a proof of the intuitive notion that the error in numerically integrating a stable equation grows less rapidly than for an unstable equation.
Difference methods for asymptotic estimates of errors at numerical integration of systems of ordinary differential equations
Application of group theory to numerical integration of motion equations of conservative dynamical system