Space-time multi-domain spectral collocation method for the Fisher’s equation

Source abstract

A space-time multi-domain Legendre-Gauss-Lobatto collocation method is developed to solve Fisher’s equation with nonhomogeneous boundary conditions, addressing aliasing errors caused by nonlinear terms. For large-scale problems in the spatial domain, a multi-domain collocation method is proposed, where appropriate boundary conditions are imposed at the common interfaces of adjacent subdomains to ensure the global smoothness of the numerical solution. A quasi-orthogonal approximation is constructed to fit both the function values at the interval endpoints and those at interior points. The convergence and stability of the scheme are analyzed using the Petrov-Galerkin spectral method with numerical integration. Numerical experiments demonstrate the effectiveness and accuracy of the proposed method.