Solving an inverse problem for a parabolic equation with a nonlocal boundary condition in the reproducing kernel space

Iranian Journal of Numerical Analysis and Optimization

مقاله 3، دوره 4، شماره 1 - شماره پیاپی 5، مرداد 2014، صفحه 57-76   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.v4i1.23266

نویسندگان

M. Mohammadi؛ R. Mokhtari^* ؛ F. T. Isfahani

Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156- 83111, Iran.

چکیده

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.

کلیدواژه‌ها

Inverse Problem؛ Parabolic equation؛ Nonlocal boundary conditions؛ Reproducing kernel space

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