Error estimates of the integral deferred correction method for stiff problems. (English) Zbl 1364.65151
The article is concerned with deferred correction methods constructed with stiffly accurate Runge-Kutta schemes for singularly perturbed initial value problems. The deferred correction scheme is based on an integral formulation of the respective error equations, taking advantage of “good” quadrature rules. The main contribution of the paper is a convergence and stability analysis of these methods, mainly based on an asymptotic expansion in powers of the perturbation parameter. Numerical experiments for the van der Pol equation illustrate the results.
Reviewer: Michael Plum (Karlsruhe)
MSC:
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
| 65-XX | Numerical analysis |
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65L04 | Numerical methods for stiff equations |
| 65B05 | Extrapolation to the limit, deferred corrections |
| 65L11 | Numerical solution of singularly perturbed problems involving ordinary differential equations |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
Software:
RODASReferences:
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