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Reduced Differential Transform Method for Solving Linear and Nonlinear Goursat Problem
Department of Mathematics, College of Science, Omdurman Islamic University, Khartoum, Sudan
Department of Mathematics, College of Science, AL-Neelain University, Khartoum, Sudan
- 1 Department of Mathematics, College of Science, Omdurman Islamic University, Khartoum, Sudan
- 2 Department of Mathematics, College of Science, AL-Neelain University, Khartoum, Sudan
Applied Mathematics·Volume 07 (2016)·Pages 1049–1056·Published 7 June 2016·DOI10.4236/am.2016.710092
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Abstract
In this paper a new method for solving Goursat problem is introduced using Reduced Differential Transform Method (RDTM). The approximate analytical solution of the problem is calculated in the form of series with easily computable components. The comparison of the methodology presented in this paper with some other well known techniques demonstrates the effectiveness and power of the newly proposed methodology.
KeywordsReduced Differential Transform MethodGoursat ProblemAdomian Decomposition Method (ADM)Variational Iteration Method (VIM)
- Zhou, J.K. (1986) Differential Transform and Its Applications for Electrical Circuits. Huazhong University Press, Wuhan.
- Wazwaz, A.M. (1993) On the Numerical Solution of the Goursat Problem. Applied Mathematics and Computation, 59, 89-95. http://dx.doi.org/10.1016/0096-3003(93)90036-e
- Keskin, Y., Caglar, I. and Koc, A.B. (2011) Numaerical Solution of Sine-Gordon Equation by Reduced Differential Transform Method. WEC, 1, 6-8.
- Day, J.T. (1966) A Runge-Kutta Method for the Numerical Solution of the Goursat Problem in Hyperbolic Partial Differential Equations. The Computer Journal, 9, 81-83. http://dx.doi.org/10.1093/comjnl/9.1.81
- Evans, D.J. and Sanugi, B.B. (1988) Numerical Solution of the Goursat Problem by a Nonlinear Trapezoidal Formula. Applied Mathematics Letters, 1, 221-223. http://dx.doi.org/10.1016/0893-9659(88)90080-8
- Wazwaz, A.M. (2007) The Variational Iteration Method for a Reliable Treatment of the Linear and the Nonlinear Goursat Problem. Applied Mathematics and Computation, 193, 455-462. http://dx.doi.org/10.1016/j.amc.2007.03.083
- Wazwaz, A.M. (1995) The Decomposition Method for Approximate Solution to the Goursat Problem. Applied Mathematics and Computation, 69, 299-311. http://dx.doi.org/10.1016/0096-3003(94)00137-s
- Wazwaz, A.M. (2002) Partial Differential Equations: Methods and Applications. Balkema Publishers, The Netherlands.
- Adomian, G. (1994) Solving Frontier Problems of Physics: The Decomposition Method. Kluwer, Boston. http://dx.doi.org/10.1007/978-94-015-8289-6