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

This paper studies the convergence and efficient implementation of generalized Stormer-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. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

This study investigates the convergence and efficient implementation of generalized Stormer-Cowell methods (GSCMs) when applied to large-scale second-order stiff semilinear systems. Theoretical analysis proves the uniqueness and convergence order of the GSCMs under certain conditions. Practical computation involves a linear iterative scheme for solving discretized nonlinear algebraic equations and a block triangular preconditioning strategy for solving linear systems. Numerical tests demonstrate the effectiveness of the proposed methods.