Runge–Kutta–Nyström‐type parallel block predictor–corrector methods
Copyright policy )Runge–Kutta–Nyström‐type parallel block predictor–corrector methods
The authors investigate a particular class of explicit Runge-Kutta-Nyström-type block predictor-corrector methods for use on parallel computers. The approach consists of applying the predictor-corrector method not only at step points, but also at off-step points (block points). By using direct Runge-Kutta-Nyström correctors, the authors obtain block parallel iterated Runge-Kutta-Nyström (BPIRKN) methods possessing both faster convergence and smaller truncation error. The algorithm described in the paper requires two sequential derivative evaluations per step for any order of accuracy. Comparisons with the highly efficient code ODEX2 show many advantages of BPIRKN methods.
- University of the Sciences United States
- VNU University of Science Viet Nam
- Vietnam National University, Hanoi Viet Nam
- Martin Luther University Halle-Wittenberg Germany
convergence, algorithm, second-order systems, Parallel numerical computation, error bounds, Nonlinear ordinary differential equations and systems, Runge-Kutta-Nyström methods, stability, Numerical methods for initial value problems involving ordinary differential equations, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, block predictor-corrector methods, parallel computation, Stability and convergence of numerical methods for ordinary differential equations, Error bounds for numerical methods for ordinary differential equations
convergence, algorithm, second-order systems, Parallel numerical computation, error bounds, Nonlinear ordinary differential equations and systems, Runge-Kutta-Nyström methods, stability, Numerical methods for initial value problems involving ordinary differential equations, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, block predictor-corrector methods, parallel computation, Stability and convergence of numerical methods for ordinary differential equations, Error bounds for numerical methods for ordinary differential equations
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