In the mathematical modeling of many physical phenomena, the diffusion equations with nonlocal boundary condition can be appeared. In this paper, we focus on the two-dimensional inhomogeneous diffusion equations subject to a nonlocal boundary condition. We transform the model of partial differential equation (PDE) into a system of first order, linear, ordinary differential equations (ODEs).

In this paper, we focus on the two-dimensional linear Telegraph equation with some initial and boundary conditions. We transform the model of partial differential equation (PDE) into a system of first order, linear, ordinary differential equations (ODEs). Our method is based on finding a solution in the form of a polynomial in three variables U n (x, y, t) = n i=0 n j=0 n k=0 U (i, j, k)x i y j t k with undetermined coefficients U (i, j, k). The main idea of our process is based on the differential transformation method (DTM).