Numerical solution for a class of parabolic integro-differential equations subject to integral boundary conditions

Abstract Many physical phenomena can be modelled through nonlocal boundary value problems whose conditions involve integral terms. In this work we propose a numerical algorithm, by combining second-order Crank–Nicolson schema for the temporal discretization and Legendre–Chebyshev pseudo-spectral method (LC–PSM) space discretization, to solve class of parabolic integrodifferential equations subject conditions. The approach proposed in paper is based on Galerkin formulation Legendre polynomials. Results stability convergence are established. Numerical tests presented support theoretical results demonstrate accuracy effectiveness