Semianalytical Method for Nonhomogeneous PDEs

Consider a general parabolic PDE with a source term where y is the source term 

The solution for equation (5.16) is obtained by adding the nonhomogeneous solution to the matrix exponential (Amundson, 1966 [7] Taylor and Krishna, 1993 [8] Subramanian and White, 2000 [5] see section 2.1.3)  

we obtain a semianalytical solution, i.e., the dependent variables at all the node points are obtained as an analytical solution of time t. The procedure for solving linear parabolic partial differential equations with nonhomogeneous boundary conditions can be summarized as follows  

Start the Maple program with a restart command to clear all variables. 

Call with(linalg) and with(plots) commands. 

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