Double side approach method to obtain solutions for transient nonlinear heat conduction using genetic algorithms

Authors:
Cha'o-Kuang Chen;Chen-I Hung;Zong-Yi Lee
Affiliations:
Department of Mechanical Engineering, National Cheng-Kung University, Tainan 701, Taiwan, ROC;Department of Mechanical Engineering, National Cheng-Kung University, Tainan 701, Taiwan, ROC;Department of Mechanical Engineering, National Cheng-Kung University, Tainan 701, Taiwan, ROC
Venue:
Applied Mathematics and Computation
Year:
2002

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Abstract

This paper presents a new method for treating engineering problems. The double side approach method (DSAM) is uses a mathematical programming and method of weighted residuals to obtain solutions for nonlinear differential equations. The method is a semi-exact solution. It is based on the collocation method and mathematical programming to create a bilateral inequality. For this process, the differential equation problem will be changed to a mathematical programming problem. By using the optimization method of genetic algorithms (GAs), we can get minimum and maximum solutions to satisfy inequality. One advantage of DSAM is that the demands on computer memory are less than those required when applying the finite element method. In this paper, a boundary value problem is studied as an example. The efficiency, accuracy, and simplicity of the DSAM approach are fully illustrated, indicating that the proposed method may be readily extended to solve a wide range of physical engineering problems.