In this paper, a two-dimensional heat diffusion system, which is modeled by a partial differential equation (PDE) is considered. Finite order approximations, for the infinite order PDE model, are constructed first by a direct application of the standard finite difference approximation (FD) scheme. Using tools of linear algebra, the constructed FD approximate models are reduced to computationally simpler models without any loss of accuracy. Further, the reduced approximate models are modified by replacing its poles with their respective asymptotic limits. Numerical experiments suggest that the proposed modifications improve the accuracy of the approximate models.
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