Journal of the Association of Arab Universities for Basic and Applied Sciences · 2015 · 21 citations · 22 references
Natural SciencesPhysicsComputational MechanicsComputational PhysicsDifferential EquationsApproximation MethodsNumerical AlgorithmsNumerical AnalysisNumerical Methods For Differential EquationsPerturbation MethodsPerturbation TheoryDifferential Equation SolversDiscretization Of Partial Differential EquationsNumerical Analysis Of Partial Differential EquationsNumerical Solutions Of Partial Differential EquationsPerturbation Of Nonlinear Differential EquationsSine-gordon EquationVariational Methods In Partial Differential EquationsVariational Perturbation Theory
In this paper, we practiced relatively new, analytical method known as the variational homotopy perturbation method for solving Klein–Gordon and sine-Gordon equations. To present the present method's effectiveness many examples are given. In this study, we compare numerical results with the exact solutions, the Adomian decomposition method (ADM), the variational iteration method (VIM), homotopy perturbation method (HPM), modified Adomian decomposition method (MADM), and differential transform method (DTM). The results reveal that the VHPM is very effective.
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Homotopy perturbation technique
Ji‐Huan He · Computer Methods in Applied Mechanics and Engineering · 1999 · 3.5K citations