A Class of Multiderivative Hybrid One-step Methods
Copyright policy )A Class of Multiderivative Hybrid One-step Methods
This paper presents a class of hybrid one-step methods for initial value problems of ordinary differential equations. These methods involve the \(s\)th order derivative and \(s+ 1\) free parameters. The order of the algorithms satisfy \(s+ 1\leq p\leq 2s+ 2\). First, the cofficients of the methods are constructed. Then the stability properties are studied, necessary and sufficient conditions for \(A\)-stability and \(L\)-stability are derived. Finally, some methods of order 7, 8, and 10 and numerical results are given.
- Wuyi University China (People's Republic of)
- Wuyi University China (People's Republic of)
Nonlinear ordinary differential equations and systems, numerical results, algorithms, Numerical methods for initial value problems involving ordinary differential equations, implicit method, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, \(L\)-stability, initial value problems, \(A\)-stability, hybrid one-step methods, Stability and convergence of numerical methods for ordinary differential equations
Nonlinear ordinary differential equations and systems, numerical results, algorithms, Numerical methods for initial value problems involving ordinary differential equations, implicit method, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, \(L\)-stability, initial value problems, \(A\)-stability, hybrid one-step methods, Stability and convergence of numerical methods for ordinary differential equations
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