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# Application of Residual Correction Method on Error Analysis of Numerical Solution on the non-Fourier Fin Problem

Hsiang-Wen Tang, Cha’o-Kung Chen1, Chen-Yu Chiang

Department of Mechanical Engineering, NCKU, Tainan, Taiwan, R.O.C., 701. Email: ckchen@mail.ncku.edu.tw Tel: +886-62757575#62140

Computer Modeling in Engineering & Sciences 2010, 65(1), 95-106. https://doi.org/10.3970/cmes.2010.065.095

## Abstract

Up to now, solving some nonlinear differential equations is still a challenge to many scholars, by either numerical or theoretical methods. In this paper, the method of the maximum principle applied on differential equations incorporating the Residual Correction Method is brought up and utilized to obtain the upper and lower approximate solutions of nonlinear heat transfer problem of the non-Fourier fin. Under the fundamental of the maximum principle, the monotonic residual relations of the partial differential governing equation are established first. Then, the finite difference method is applied to discretize the equation, converting the differential equation into the mathematical programming problem. Finally, based on the Residual Correction Method, the optimal solution under the constraints of inequalities can be obtained. The methodology of incorporating the Residual Correction Method into the nonlinear iterative procedure of the finite difference will make it easier and faster to obtain upper and lower approximate solutions and can save the computing time, reduce the storage of memory and avoid unnecessary repeated testing.

## Keywords

Tang, H., Chen, C., Chiang, C. (2010). Application of Residual Correction Method on Error Analysis of Numerical Solution on the non-Fourier Fin Problem. CMES-Computer Modeling in Engineering & Sciences, 65(1), 95–106.

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