Convergence of linear multistep and one-leg methods for stiff nonlinear initial value problems. (English) Zbl 0724.65071
The convergence of linear multistep and one-leg methods is studied for stiff nonlinear initial value problems: \(u'(t)=f(t,u(t)),\quad (0<t\leq T),\quad u(0)\quad given,\) with \(u(0)\in {\mathbb{R}}^ m\) and \(f:[0,T]\times {\mathbb{R}}^ m\to {\mathbb{R}}^ m.\)
Estimates for local errors are given for the two methods. Global error bounds are derived, also, for one-leg and linear multistep methods for nonlinear initial value problems of arbitrary stiff. Under suitable stability assumptions the multistep methods have similar orders of convergence for stiff and nonstiff problems provided that the stepsize variation is sufficiently regular.
Estimates for local errors are given for the two methods. Global error bounds are derived, also, for one-leg and linear multistep methods for nonlinear initial value problems of arbitrary stiff. Under suitable stability assumptions the multistep methods have similar orders of convergence for stiff and nonstiff problems provided that the stepsize variation is sufficiently regular.
Reviewer: M.Gousidou-Koutita (Thessaloniki)
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65L50 | Mesh generation, refinement, and adaptive methods for ordinary differential equations |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 34E13 | Multiple scale methods for ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
Keywords:
variable stepsize; one-leg methods; stiff nonlinear initial value problems; Global error bounds; linear multistep methods; orders of convergenceSoftware:
RODASReferences:
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