A new procedure of initial boundary value problems using homotopy perturbation method
DOI:
https://doi.org/10.31642/JoKMC/2018/010708Keywords:
initial boundary value problems, homotopy perturbation method.Abstract
In this paper, , a new procedure is applied to treatment of initial boundary value problems by mixed initial and boundary conditions together  to obtain a new initial solution at every iteration using homotopy perturbation method. The structure of a new successive initial solutions can give a more accurate solution. Some examples (linear and nonlinear, homogeneous and nonhomogeneous problems) are given in this paper to illustrate the effectiveness and convenience of a new procedure.
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Wazwaz A.M.,2002 “The decomposition method for solving higher dimensional initial boundary value problems of variable coefficients,” International Journal of Computer Mathematics 76(2) , 159-172. DOI: https://doi.org/10.1080/00207160008805017
Wazwaz A.M., 1995“On the solution of the fourth order parabolic equation by the decomposition method”, Intern. J. ComputerMath., 57, 213-217. DOI: https://doi.org/10.1080/00207169508804424
Wazwaz A.M.,2001 “Analytic treatment for variable coefficient fourth-order parabolic partial differential equations”, Applied Mathematics and Computation, 123 (2), 219-227. DOI: https://doi.org/10.1016/S0096-3003(00)00070-9
Momani S.,2005 “Analytical approximate solution for fractional heat-like and wave-like equations with variable coefficients using the decomposition method”. Applied Mathematics and Computation 165, 459–472. DOI: https://doi.org/10.1016/j.amc.2004.06.025
Yulita Molliq R, Noorani M.S.M., Hashim I.,2009 “Variational iteration method for fractional heat- and wave-like equations”, Nonlinear Analysis: Real World Applications 10, 1854-1869. DOI: https://doi.org/10.1016/j.nonrwa.2008.02.026
Noor M.A. and Mohyud-Din S.T.,2008 “Solving Higher Dimensional Initial Boundary Value Problems by Variational Iteration Decomposition Method”, Applications and Applied Mathematics An International Journal 3(2), 254-266. DOI: https://doi.org/10.1155/2008/696734
Biazar J. and Aminikhah H., 2009 “Exact and numerical solutions for non-linear Burger's equation by VIM”, Mathematical and Computer Modelling 49, 1394-1400. DOI: https://doi.org/10.1016/j.mcm.2008.12.006
Shidfar A. and Molabahrami A.,2010 “A weighted algorithm based on the homotopy analysis method: Application to inverse heat conduction problems”, Commun Nonlinear SciNumerSimulat15,2908-2915. [9] Niu Z. and Wang C., 2010“A one-step optimal homotopy analysis method for nonlinear differential equations”, Commun Nonlinear Sci Numer Simulat 15, 2026-2036. DOI: https://doi.org/10.1016/j.cnsns.2009.11.011
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Copyright (c) 2013 Abeer Majeed Jassim, Elaf Jaafar Ali, Afrah Abd-Imam Ahmed
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