Mixed Jacobi-Fourier spectral method for Fisher equation

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.

Keywords

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