Radial Basis Function Quasi-interpolation Methods for Solving a Kind of Inverse Problems

Abstract: this thesis is divided into three parts. The first part review some results about inverse problem concerning background, theories, numerical methods. In the second part, a class of qusi-interpolation operators is given. The last part present a scheme using RBF qusi-interpolation method to find the solution of an inverse problem with source control parameter and determine this source control parameter, and approximation order, moreover, some numerical examples is given. The method of RBF being used for finding the solution of an inverse problem with source control parameter and determining this source control parameter is a new application of RBF theories. Because a much wider range physical phenomena is modeled by nonclassical parabolic initial-boundary value problems, theoretical behavior and numerical approximation of these problems have been active areas of research. Based on the idea of RBF approximation, a fast and high accurate numerical method is developed for solving an inverse problem with control parameter. It has been shown to be effective…
Key words: Radial Basis Function; Quasi-interpolation; Inverse Problem; Source Parameter

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