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

作者：Hao Chen^*; Yeru Yang

来源：APPLIED MATHEMATICS AND COMPUTATION, 2021, 400: 126062.

DOI：10.1016/j.amc.2021.126062

• Second-order semilinear ordinary differential equations
• Generalized Störmer-Cowell methods
• Boundary value methods
• Convergence
• Preconditioner

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.