فهرست مطالب
Computational Methods for Differential Equations
Volume:2 Issue: 2, Spring 2014
- تاریخ انتشار: 1393/01/12
- تعداد عناوین: 7
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Pages 62-68In this paper, we present Legendre wavelet method to obtain numerical solution of a singular integro-differential equation. The singularity is assumed to be of the Cauchy type. The numerical results obtained by the present method compare favorably with those obtained by various Galerkin methods earlier in the literature.Keywords: Legendre wavelet, Singular integro-differential equation, Cauchy type
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Pages 69-76The first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. This method can be applied to non integrable equations as well as to integrable ones. In this paper, the first integral method is used to construct exact solutions of the 2D Ginzburg-Landau equation.Keywords: Exact solutions, First integral method, 2D Ginzburg-Landau equation
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Pages 77-82In this work, we successfully construct the new exact traveling wave solutions of the generalized Sinh–Gordon equation by new application of the homogeneous balance method. The idea introduced in this paper can be applied to other nonlinear evolution equations.Keywords: Solitary wave solution, Homogeneous balance method, generalized sine-Gordon equation
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Pages 83-90The extended homogeneous balance method is used to construct exact traveling wave solutions of the Maccari system, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation. Many exact traveling wave solutions of the Maccari system equation are successfully obtained.Keywords: Extended homogeneous balance method, Maccari system, Riccati equation, Soliton-like solution, Periodic-like solution
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Pages 91-98In this paper, a new implicit nonstandard finite difference scheme for conservation laws, which preserving the property of TVD (total variation diminishing) of the solution, is proposed. This scheme is derived by using nonlocal approximation for nonlinear terms of partial differential equation. Schemes preserving the essential physical property of TVD are of great importance in practice. Such schemes are free of spurious oscillations around discontinuities. Numerical results for Burger's equation is presented. Comparison of numerical results with a classical difference scheme is given.Keywords: Nonstandard finite difference scheme, Total variation diminishing, Conservation law, Nonlocal approximation
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Pages 99-114In this paper, we solve a inhomogeneous fractional Klein-Gordon equation by the method of separating variables. We apply the method for three boundary conditions, contain Dirichlet, Neumann, and Robin boundary conditions, and solve some examples to illustrate the effectiveness of the method.Keywords: Fractional Klein-Gordon equation, Mittag-Leffler, Method of separating variables, Caputo derivative
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Pages 115-122The homogeneous balance method can be used to construct exact traveling wave solutions of nonlinear partial differential equations. In this paper, this method is used to construct new soliton solutions of the (3+1) Jimbo--Miwa equation.Keywords: Homogeneous balance method, (3+1) Jimbo–Miwa equation, Solitary wave solutions