The generalized approximation method and nonlinear heat transfer equations

R. A. Khan, Centre for Advanced Mathematics and Physics, NUST, Rawalpindi, Pakistan

E. J. Qualitative Theory of Diff. Equ., No. 2. (2009), pp. 1-15.

Abstract: Generalized approximation technique for a solution of one-dimensional steady state heat transfer problem in a slab made of a material with temperature dependent thermal conductivity, is developed. The results obtained by the generalized approximation method (GAM) are compared with those studied via homotopy perturbation method (HPM). For this problem, the results obtained by the GAM are more accurate as compared to the HPM. Moreover, our (GAM) generate a sequence of solutions of linear problems that converges monotonically and rapidly to a solution of the original nonlinear problem. Each approximate solution is obtained as the solution of a linear problem. We present numerical simulations to illustrate and confirm the theoretical results.

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