A super accurate shifted Tau method for numerical computation of the Sobolev-type differential equation with nonlocal boundary conditions

In this article, we propose a super accurate numerical scheme to solve the one-dimensional Sobolev type partial differential equation with an initial and two nonlocal integral boundary conditions. Our proposed methods are based on the shifted Standard and shifted Chebyshev Tau method. Firstly, We convert the model of partial differential equation to a linear algebraic equation and then we solve this system. Shifted Standard and shifted Chebyshev polynomials are applied for giving the computational results. Numerical results are presented for some problems to demonstrate the usefulness and accuracy of this approach. The method is easy to apply and produces very accurate numerical results.