Enhanced two-dimensional differential transform method for solving homogenous Dirichlet problems; Application: heat transfer in bars

Authors

1 Faculty of Engineering, Ferdowsi University of Mashhad, Iran

2 Department of Civil Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Iran

Abstract

In this article, a new method has been proposed to enhance two-dimensional differential transform method (2D-DTM) for solving initial boundary value problems (IBVPs) including partial differential equations (PDEs) with homogeneous Dirichlet boundary conditions. The method is inspired by the Ritz method which is utilized in variational calculus. To this end, multiplying the basic relation of DTM by specific functions which satisfy the boundary conditions, would resolve the weakness of the classical version of 2D-DTM in precisely satisfying the boundary conditions. Obviously, implementing this will change the governing relations of the classical DTM, such as recursive formula related to differential equation of the problem. It should be mentioned that, these changes are comprehensively described in the article. Moreover, to show the robustness of the proposed method, two heat transfer problems in the bars are thoroughly solved by classical and enhanced DTM and the results are compared with the exact solutions. The thermal diffusivity of the bar is considered constant and spatially varied in mentioned problems. The numerical results show the accuracy of the proposed method, especially in satisfying the homogeneous Dirichlet boundary conditions of the problem.

Keywords

References

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Journal of Solid and Fluid Mechanics
Volume 9, Issue 4
December 2019
Pages 209-226

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