On convergence and stability conditions of homotopy perturbation method for an inverse heat conduction problem

Iranian Journal of Numerical Analysis and Optimization

مقاله 6، دوره 5، شماره 2 - شماره پیاپی 8، دی 2015، صفحه 75-93   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.v5i2.40594

نویسندگان

Q. ‎Jannati؛ A. Zakeri^*

Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran.

چکیده

In this paper, we investigate the application of the Homotopy Perturbation Method (HPM) for solving a one-dimensional nonlinear inverse heat conduction problem. In this problem the thermal conductivity term is a linear function with respect to unknown heat temperature in bounded interval. Furthermore, the temperature histories are unknown at the end point of the interval. This problem is ill-posed. So, using the finite difference scheme and discretizing the time interval, the partial differential equation is reduced into a System of Nonlinear Ordinary Differential Equations (SNODE's). Then, using HPM, the approximated solution of the obtained Ordinary Differential Equation (ODE) system is determined. In the sequel, the stability andconvergence conditions of the proposed method are investigated. Finally, anupper bound of the error is provided.

کلیدواژه‌ها

Homotopy perturbation method؛ Diffusion equation؛ Disceretiz- ing method؛ Inverse Problem

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