Legendre-Chebyshev pseudo-spectral method for the diffusion equation with non-classical boundary conditions

The present paper is devoted to the numerical approximation for the diffusion equation subject to non-local boundary conditions. For the space discretization, we apply the Legendre-Chebyshev pseudospectral method, so that, the problem under consideration is reduced to a system of ODEs which can be solved by the second order Crank-Nicolson schema. Optimal error estimates for the semi-discrete scheme are derived in L²-norm. Numerical tests are included to demonstrate the effectiveness of the proposed method.