This paper reveals an innovative technique built on variational iteration method and Laplace transformation, called modified Laplace variational iteration method. At first, we apply variational iteration method, and then, Laplace transformation is introduced to calculate the Lagrange multipliers. An innovation of this algorithm shows that Lagrange multiplier has carried out in the absence of integration used in variational iteration method and without taking convolution theorem use in Laplace transform. Furthermore, He’s polynomials are calculated by applying homotopy perturbation method to overcome the nonlinear terms arising in the problems. The proposed method points out that the derived solution exists without any linearization, discretization or any kind of hypothesis. Some numerical models are illustrated which shows the compactness and reliableness of this method.
M-LVIM He’s polynomials Laplace transform Klein–Gordon and Sine–Gordon Equations
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This work is supported by National Natural Science Foundation of China (Grant No: 11571057).
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