Research and application of compact finite difference method of low reaction-diffusion equation

Huancheng Zhang, Guanchen Zhou

Abstract

The paper describes the theory of fractional derivative and specific application examples in the field of engineering sciences. On this basis, this paper mainly studies the low reaction-diffusion equations. First using compact operator, the paper constructs a higher-order finite difference scheme. Then the paper proves the existence and uniqueness of the difference solution by matrix method and analyzes the stability and convergence of the scheme by Fourier method.