Space-time spectral method for two-dimensional semilinear parabolic equations (Q2809490)

This paper focuses on a numerical approximation of a two-dimensional semilinear parabolic equation with the aid of a higher-order method. The numerical method is based on a combination of the Galerkin-Legendre spectral method application for discretization of the spatial derivatives and the spectral collocation method for the time integration. The method allows arbitrary high order of accuracy in both space and time. The optimal a priori error bound in the \(L^2\) norm is proven for the semi-discrete formulation. Numerical results are shown to demonstrate the convergence and accuracy of the method.