solving an inverse problem for a parabolic equation with a nonlocal boundary condition in the reproducing kernel space
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abstract
on the basis of a reproducing kernel space, an iterative algorithm for solving the inverse problem for heat equation with a nonlocal boundary condition is presented. the analytical solution in the reproducing kernel space is shown in a series form and the approximate solution vn is constructed by truncating the series to n terms. the convergence of vn to the analytical solution is also proved. results obtained by the proposed method imply that it can be considered as a simple and accurate method for solving such inverse problems.
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Journal title:
iranian journal of numerical analysis and optimizationجلد ۴، شماره ۱، صفحات ۵۷-۰
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