On the Stability of a Variable Step Exponential Splitting Method for Solving Multidimensional Quenching-Combustion Equations

Abstract

This paper concerns the numerical stability of a splitting scheme for solving the three-dimensional degenerate quenching-combustion equation. The diffusiontype nonlinear equation possess highly nonlinear source terms, and is extremely important to the study of numerical combustions. Arbitrary fixed nonuniform spatial grids, which are not necessarily symmetric, are considered in our investigation. The numerical solution is advanced through a semi-adaptive exponential splitting strategy. The temporal adaptation is achieved via a suitable arc-length monitoring mechanism. Criteria for preserving the linear numerical stability of the decomposition method is proven under the spectral norm. A new stability criterion is proposed.