An Exact solution of Diffusion Equation with boundary conditions by Pad\'{e}-Laplace Differential Transform Method


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Authors

  • Kiranta Kumari Department of Mathematics & Statistics, Banasthali University, Banasthali, Rajasthan, India
  • Praveen Kumar Gupta Department of Mathematics, National Institute of Technology, Silchar, Assam, India
  • Gauree Shanker Department of Mathematics & Statistics, Banasthali University, Banasthali, Rajasthan, India

Keywords:

Diffusion equation, Boundary condition, Laplace transforms, DTM, LDTM, Pade approximation

Abstract

In this paper, we solve Diffusion equation with boundary conditions analytically by using a combined form of Laplace transform method and differential transform method (DTM) and Pade approximation. The aim of using the Laplace transform is to overcome the deficiency that is caused by unsatisfied boundary conditions in using differential transform method. The combined method is capable to handle diffusion equation with boundary conditions. The solutions obtained by proposed method are compared with the known exact solutions and found that our solutions are in good agreement with the known exact solutions. The obtained results show the simplicity of proposed method and massive reduction in calculations.

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Published

10-12-2015

How to Cite

Kiranta Kumari, Praveen Kumar Gupta, & Gauree Shanker. (2015). An Exact solution of Diffusion Equation with boundary conditions by Pad\’{e}-Laplace Differential Transform Method. International Journal of Mathematics And Its Applications, 3(4 - B), 1–8. Retrieved from http://ijmaa.in/index.php/ijmaa/article/view/490

Issue

Vol. 3 No. 4 - B (2015)

Section

Research Article

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.