Application of Homotopy Perturbation Transform Method for Solving Linear and Nonlinear Klein-Gordon Equations
Application of Homotopy Perturbation Transform Method for Solving Linear and Nonlinear Klein-Gordon Equations
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发表时间：
2012
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通讯作者：
Jagdev Singh;Devendra Kumar;S. Rathore;J. Nath
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作者：
Jagdev Singh;Devendra Kumar;S. Rathore;J. Nath
本文应用同伦摄动变换方法(HPTM)求解线性和非线性Klein-Gordon方程。同伦摄动变换法是拉普拉斯变换法和同伦摄动法的结合形式。该方案无需任何离散化或限制性假设即可找到解，避免了舍入误差。这种方法不需要使用Adomian多项式来解决非线性问题，这一事实可以认为是该方法相对于分解方法的一个明显优势。结果表明，该算法效率高、计算简单，可推广应用于其他非线性问题。
In this paper, the homotopy perturbation transform method (HPTM) has been applied to obtain the solution of the linear and nonlinear Klein-Gordon equations. The homotopy perturbation transform method is a combined form of the Laplace transform method with the homotopy perturbation method. This scheme finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. The fact that this technique solves nonlinear problems without using Adomian's polynomials can be considered as a clear advantage of this technique over the decomposition method. The results reveal that the proposed algorithm is very efficient, simple and can be applied to other nonlinear problems.