Numerical solution of time-dependent diffusion equations with nonlocal boundary conditions via a fast matrix approach

Abstract

This article contributes a matrix approach by using Taylor approximation to obtain the<br><br>numerical solution of one-dimensional time-dependent parabolic partial differential equations<br><br>(PDEs) subject to nonlocal boundary integral conditions. We first impose the initial and boundary<br><br>conditions to the main problems and then reach to the associated integro-PDEs. By using operational<br><br>matrices and also the completeness of the monomials basis, the obtained integro-PDEs will<br><br>be reduced to the generalized Sylvester equations. For solving these algebraic systems, we apply a<br><br>famous technique in Krylov subspace iterative methods. A numerical example is considered to show<br><br>the efficiency of the proposed idea.