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Mixed Jacobi-Fourier spectral method for Fisher equation

    Yujian Jiao Affiliation
    ; Tianjun Wang Affiliation
    ; Xiandong Shi Affiliation
    ; Wenjie Liu Affiliation

Abstract

In this paper, we propose a mixed Jacobi-Fourier spectral method for solving the Fisher equation in a disc. Some mixed Jacobi-Fourier approximation results are established, which play important roles in numerical simulation of various problems defined in a disc. We use the generalized Jacobi approximation to simulate the singularity of solution at the regional center. This also simplifies the theoretical analysis and provides a sparse system. The stability and convergence of the proposed scheme are proved. Numerical results demonstrate the efficiency of this new algorithm and coincide well with the theoretical analysis.

Keyword : Fisher equation in a disc, mixed Jacobi-Fourier approximation, spectral method, problem with end-point weak singularity, nonlinear problem

How to Cite
Jiao, Y., Wang, T., Shi, X., & Liu, W. (2018). Mixed Jacobi-Fourier spectral method for Fisher equation. Mathematical Modelling and Analysis, 23(2), 240-261. https://doi.org/10.3846/mma.2018.016
Published in Issue
Apr 18, 2018
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