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Direct solution of ill-posed boundary value problems by radial basis function collocation method. (English) Zbl 1108.65059
Summary: Numerical solution of ill-posed boundary value problems normally requires iterative procedures. In a typical solution, the ill-posed problem is first converted to a well-posed one by assuming the missing boundary values. The new problem is solved by a conventional numerical technique and the solution is checked against the unused data. The problem is solved iteratively using optimization schemes until convergence is achieved. The present paper offers a different procedure. Using the radial basis function collocation method, we demonstrate that the solution of certain ill-posed problems can be accomplished without iteration. This method not only is efficient and accurate, but also circumvents the stability problem that can exist in the iterative method.

65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
Full Text: DOI
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