Document Zbl 1533.65096

A stiff-cut splitting technique for stiff semi-linear systems of differential equations. (English) Zbl 1533.65096

Numer. Algorithms 95, No. 3, 1387-1412 (2024).

Summary: In this paper, we study a new splitting method for the semi-linear system of ordinary differential equation, where the linear part is stiff. Firstly, the stiff part is split into two parts. The first stiff part, that is called the stiff-cutter and expected to be easily inverted, is implicitly treated. The second stiff part and the remaining nonlinear part are explicitly treated. Therefore, such stiff-cut method can be fast implemented and save the CPU time. Theoretically, we rigorously prove that the proposed method is unconditionally stable and convergent, if the stiff-cutter is chosen to be well-matched in the stiff part. As an application, we apply our method to solve a spatial-fractional reaction-diffusion equation and give a way for how to choose a suitable stiff-cutter. Finally, numerical experiments are carried out to illustrate the accuracy and efficiency of the proposed stiff-cut method.

Cited in 1 Document

MSC:

65L04	Numerical methods for stiff equations
65L05	Numerical methods for initial value problems involving ordinary differential equations
65L20	Stability and convergence of numerical methods for ordinary differential equations
65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs

Keywords:

stiff ordinary differential equations; stiff-cut schemes; convergence analysis; stability analysis

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