Double Laplace Transform Combined with Iterative Method for Solving Non-Linear Telegraph Equation

Jump To References Section

Authors

  • Ranjit R. Dhunde
     Department of Mathematics, Datta Meghe Institute of Engineering, Technology and Research, Wardha, M.S. ,IN
  • G. L. Waghmare
     Department of Mathematics, Government Science College, Gadchiroli, M.S. ,IN

Keywords:

Double Laplace Transform, Inverse Laplace Transform, Iterative Method, Nonlinear Partial Differential Equation, Non-Linear Telegraph Equation.

Abstract

In the present paper, double Laplace transform combined with Iterative method is applied to solve nonlinear Telegraph equation. Illustrative examples are solved to demonstrate the efficiency of the method.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Downloads

Published

2016-12-01

How to Cite

Dhunde, R. R., & Waghmare, G. L. (2016). Double Laplace Transform Combined with Iterative Method for Solving Non-Linear Telegraph Equation. The Journal of the Indian Mathematical Society, 83(3-4), 221–230. Retrieved from https://informaticsjournals.co.in/index.php/jims/article/view/6605

Issue

Volume 83, Issue 3-4, July-December 2016

Section

Articles

License

Copyright (c) 2016 Ranjit R. Dhunde, G. L. Waghmare

Creative Commons License

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

 

References

S. Abbasbandy, H. Roohani Ghehsareh, A New Semi-Analytical solution of the Telegraph equation with integral condition, Z. Naturforsch. 66a, 760-768 (2011).

J. Biazar, H. Ebrahimi, An approximation to the solution of Telegraph equation by Adomain decomposition method, International Mathematical Forum, 2, 2007, No. 45.

J. Biazar, H. Ebrahimi, Z. Ayati, An Approximation to the solution of telegraph equation by variational iteration method, Numerical methods for partial differential equations, 2008.

L. Debnath, The double Laplace transforms and their properties with applications to Functional, Integral and Partial Differential Equations, Int. J. Appl. Comput. Math, 2015.

M. Dehghan, A. Ghesmati, Solution of the second order one dimensional hyperbolic telegraph equation by using the dual reciprocity boundary integral equation (DRBIE) method, Engineering Analysis with Boundary Elements, Vol. 34, No. 19, pp. 1011210121, 2013.

H. Eltayeb, A. Kilicman, A Note on Double Laplace Transform and Telegraphic Equations, Abstract and Applied Analysis, Volume 2013.

Varsha Daftardar-Gejji, Hossein Jafari, An iterative method for solving nonlinear functional equations, J. Math. Anal. Appl. 316 (2006), 753-763.

J. H. He, Variational iteration method- a kind of non-linear analytical technique: some examples, Int. J. of Non-linear Mechanics 34, 699-708, 1999.

J. H. He, Homotopy perturbation method: a new nonlinear analytical technique, Appl. Math. Comput. 135(1), 73-79 (2003).

Y. Keskin, G. Oturanc, Reduced differential transform method for partial differential equations, International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 10, no. 6, pp. 741-749, 2009.

R. C. Mittal, Rachna Bhatia, A Collocation method for numerical solution of hyperbolic telegraph equation with Neumann boundary conditions, International Journal of Computational Mathematics, Volume 2014.

P. W. Partridge, C. A. Brebbia, L. C. Wrobel, The dual reciprocity boundary element method, Southampton, Boston: Computational Mechanics Publications, Elsevier, 1962.

B. Raftari, A. Yildirim, Analytical solution of second-order hyperbolic Telegraph equation by Variational Iteration and Homotopy Perturbation methods, Results in Mathematics, 2010.

V. K. Srivastava, M. K. Awasthi, R. K. Chaurasia, M. Tamsir, The telegraph equation and its solution by Reduced Differential Transform Method, Modelling and Simulation in Engineering, Volume 2013.

Ian N. Sneddon, The Use of Integral Transforms , Tata Mcgraw Hill Edition 1974.