Analysis of Immersed Interface Difference Schemes for Reaction-diffusion Problems with Singular Own Sources

Abstract

Abstract This paper analyzes immersed interface difference schemes for onedimensional reaction-diffusion equations with singular own linear and nonlinear sources. Error bounds in the infinity norm based on the maximum principle are derived. Sharper bounds and a more detailed structure of the error are obtained using the asymptotic error expansion analysis method. Numerical examples confirm the theoretical results.