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