ERROR ANALYSIS OF LEGENDRE-GALERKIN SPECTRAL METHOD FOR A PARABOLIC EQUATION WITH DIRICHLET-TYPE NON-LOCAL BOUNDARY CONDITIONS

An efficient Legendre-Galerkin spectral method and its error analysis for a one-dimensional parabolic equation with Dirichlet-type non-local boundary conditions are presented in this paper. The spatial discretization is based on Galerkin formulation the Legendre orthogonal polynomials, while time derivative discretized by using symmetric Euler finite difference schema. stability convergence of semi-discrete approximation rigorously set up following novel approach to overcome difficulties caused non-locality condition. Several numerical tests included confirm efficacy proposed support theoretical results.