Space-time spectral method for a weakly singular parabolic partial integro-differential equation on irregular domains

摘要

The spectral method is proposed for the partial integro-differential equations with a weakly singular kernel on irregular domains. The space discretization is based on the nodal spectral element method using the Lagrange polynomials basis associated with the Gauss-Lobatto-Legendre quadrature nodes. Also the model is discretized in time with the Legendre spectral Galerkin method. The discretization leads to conversion of the problem to a Sylvester matrix equation which can be solved efficiently by the QZ algorithm (Gardiner et al., 1992). The convergence of the method is proven by providing a priori L~2-error estimate. Numerical results illustrate the efficiency and spectral accuracy of the proposed method.