Improved multistep method with non‐linear corrections
Copyright policy )Improved multistep method with non‐linear corrections
AbstractA new semi‐implicit class of multistep methods for stiff ordinary differential equations is presented. The general method is based on the application of estimation functions not only for the derivatives but also for the state variables. This permits the transformation of the original system in a purely algebraic system using the solutions of previous steps. The novelty introduced is a non‐linear correction for the estimation‐function coefficients, which is deduced from a combined analysis of stability and convergence order. That is, the estimation‐function coefficients are recalculated in each time step. The convergence order of the resulting scheme is better than the equivalent linear multistep methods, while preserving A‐stability. Numerical experiments are presented comparing the new method with backward differentiation formula. Copyright © 2008 John Wiley & Sons, Ltd.
multistep methods, stiff systems, Nonlinear ordinary differential equations and systems, Numerical methods for initial value problems involving ordinary differential equations, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, non-linear correction, A-stability, convergence order, numerical experiments, Stability and convergence of numerical methods for ordinary differential equations
multistep methods, stiff systems, Nonlinear ordinary differential equations and systems, Numerical methods for initial value problems involving ordinary differential equations, Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, non-linear correction, A-stability, convergence order, numerical experiments, Stability and convergence of numerical methods for ordinary differential equations
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