Generalized Störmer-Cowell methods with efficient iterative solver for large-scale second-order stiff semilinear systems

Hao Chen and Yeru Yang

Applied Mathematics and Computation, 2021, vol. 400, issue C

Abstract: This paper studies the convergence and efficient implementation of generalized Störmer-Cowell methods (GSCMs) when they are applied to large-scale second-order stiff semilinear systems with the stiffness contained in the linear part. Theoretically, we prove that under some conditions the GSCMs are uniquely solvable and convergent of order p, where p is the consistence order of the methods. In practical computation, the discretized nonlinear algebraic equations can be implemented by a linear iterative scheme which is shown to be convergent. Meanwhile, a block triangular preconditioning strategy is proposed to solve the associated linear systems. Numerical tests are given to illustrate the effectiveness of the methods.

Keywords: Second-order semilinear ordinary differential equations; Generalized Störmer-Cowell methods; Boundary value methods; Convergence; Preconditioner (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:400:y:2021:i:c:s0096300321001107

DOI: 10.1016/j.amc.2021.126062

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