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Paper IPM / M / 8725  


Abstract:  
In this work, the solution of an inverse problem concerning a diffusion equation with source control parameters is presented. The homotopy perturbation method is employed to solve this equation. This method changes a difficult problem into a simple problem which can be easily solved. In this procedure, according to the homotopy technique, a homotopy with an embedding parameter p ∈ E [0, 1] is constructed, and this parameter is considered a 'small parameter', so the method is called the homotopy perturbation method, which can take full advantage of the traditional perturbation method and homotopy technique. The approxi�mations obtained by the proposed method are uniformly valid not only for small parameters, but also for very large parameters. The fact that this technique, in contrast to the traditional perturbation methods, does not require a small parameter in the system, leads to wide applications in nonlinear equations.
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