Refine your search
Collections
Co-Authors
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z All
Waghmare, G. L.
- Double Laplace Transform Combined with Iterative Method for Solving Non-Linear Telegraph Equation
Abstract Views :463 |
PDF Views:3
Authors
Affiliations
1 Department of Mathematics, Datta Meghe Institute of Engineering, Technology and Research, Wardha, M.S., IN
2 Department of Mathematics, Government Science College, Gadchiroli, M.S., IN
1 Department of Mathematics, Datta Meghe Institute of Engineering, Technology and Research, Wardha, M.S., IN
2 Department of Mathematics, Government Science College, Gadchiroli, M.S., IN
Source
The Journal of the Indian Mathematical Society, Vol 83, No 3-4 (2016), Pagination: 221-230Abstract
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.Keywords
Double Laplace Transform, Inverse Laplace Transform, Iterative Method, Nonlinear Partial Differential Equation, Non-Linear Telegraph Equation.
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.
- Solutions of Some Linear Fractional Partial Differential Equations in Mathematical Physics
Abstract Views :402 |
PDF Views:2
Authors
Affiliations
1 Department of Mathematics, Datta Meghe Institute of Engineering Technology and Research, Wardha, M.S., IN
2 Department of Mathematics, Government Science College, Gadchiroli, M.S., IN
1 Department of Mathematics, Datta Meghe Institute of Engineering Technology and Research, Wardha, M.S., IN
2 Department of Mathematics, Government Science College, Gadchiroli, M.S., IN
Source
The Journal of the Indian Mathematical Society, Vol 85, No 3-4 (2018), Pagination: 313-327Abstract
In this article, we use double Laplace transform method to find solution of general linear fractional partial differential equation in terms of Mittag-Leffler function subject to the initial and boundary conditions. The efficiency of the method is illustrated by considering fractional wave and diffusion equations, Klein-Gordon equation, Burger’s equation, Fokker-Planck equation, KdV equation, and KdV-Burger’s equation of mathematical physics.Keywords
Double Laplace Transform, Inverse Laplace Transform, Fractional Partial Differential Equation, Caputo Fractional Derivatives.References
- L. Debnath and D. Bhatta, Solutions to few linear fractional inhomogeneous partial differential equations in fluid mechanics, Fractional Calculus and Applied Analysis, volume 7, number 1, 2004.
- Z. Odibat and S. Momani, The variational iteration method: an efficient scheme for handling fractional partial differential equations in fluid mechanics, Computers and Mathematics with Applications, volume 58, 2199-2208, 2009.
- M. Dehghan, J. Manaan, and A. Saadatmandi, The solution of the linear fractional partial differential equations using the homotopy analysis method, Z. Naturforsch., 65a, 935-949, 2010.
- A. Anwar, F. Jarad, D. Baleanu and F. Ayaz, Fractional caputo heat equation within the double Laplace transform, Romanian Journal Physics, volume 58, no. 1-2, pp.15-22, 2013.
- Ranjit R. Dhunde and G. L. Waghmare, Double Laplace transform method for solving space and time fractional telegraph equations, International Journal of Mathematics and Mathematical sciences, volume 2016, Article ID 1414595, 7 pages, 2016.
- S. Momani and Z. Odibat, A novel method for nonlinear fractional partial differential equations: Combination of DTM and generalized Taylor's formula, Journal of Computational and Applied Mathematics, volume 220, pp. 85-95, 2008.
- Ranjit R. Dhunde and G. L. Waghmare, Double Laplace transform method in mathematical physics, International Journal of Theoretical and Mathematical Physics, volume 7, Issue 1, 2017, pp. 14-20.
- Ian N. Sneddon, The use of integral transforms, Tata Mcgraw Hill Edition, 1974.
- L. Debnath, The double Laplace transforms and their properties with applications to functional, integral and partial differential equations, International Journal of Applied and Computational Mathematics, vol. 2, no. 2, pp. 223-241, 2016.
- I. Podlubny, Fractional Differential equations, Academic Press, New York, 1999.
- J. Song, F. Yin, X. Cao, and F. Lu, Fractional variational iteration method versus Adomian's decomposition method in some fractional partial differential equations, Journal of Applied Mathematics, volume 2013, Article ID 392567, 10 pages, 2013.
- A. A. Elbeleze, A. Kilicman, and B. M. Taib, Fractional Variational Iteration Method and its application to fractional partial differential equation, Mathematical Problems in Engineering, volume 2013, Article ID 543848, 10 pages, 2013.
- A. A. Hemeda, Modied homotopy perturbation method for solving fractional differential equations, Journal of Applied Mathematics, volume 2014, Article ID 594245, 9 pages, 2014.
- A. S. V. Ravi Kant, and K. Aruna, Solution of fractional third-order dispersive partial differential equations, Egyptian Journal of Basic and Applied Sciences, volume 2, 2015, pp. 190-199.