In many applications such as heat diffusion and flow problems, it is of interest to describe the process behavior inside a particular medium. An example can be the strive for estimating certain parameters related to the material. These processes are often modeled by a partial differential equation. Certain methods for identifying unknown material constants require the model to be of finite order. This thesis describes how the diffusion process can be approximated with finite order model, and how the accuracy of an estimated model depends on the model order. In particular, a detailed analysis is carried out for the case when the approximate model accounts for solving the diffusion by a difference method.
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