Inverse problem of diffusion equation by He's homotopy perturbation method
Inverse problem of diffusion equation by He's homotopy perturbation method
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DOI：
10.1088/0031-8949/75/4/031
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发表时间：
2007-03
期刊：
影响因子：
2.9
通讯作者：
F. Shakeri;M. Dehghan
中科院分区：
文献类型：
--
作者：
F. Shakeri;M. Dehghan
抛物型反问题产生于物理学的许多领域，在科学和工程的各个分支中起着非常重要的作用。在过去的几年中，已经花费了相当大的努力，制定准确和有效的方法来解决这些方程。在本研究中，我们利用同伦微扰法来求解一个反抛物型方程，并计算一个未知的时变参数。同伦扰动技术是一种求解微分方程解的分析方法，其基础是构造具有嵌入参数p [0，1]（被认为是“扩展参数”）的同伦。本文对这一技术的应用及最新进展作了简要介绍。将该方法应用于所研究的抛物型反问题的结果表明了该方法的高精度、简单和有效性。
Inverse problems of parabolic type arise from many fields of physics and play a very important role in various branches of science and engineering. In the last few years, considerable efforts have been expended in formulating accurate and efficient methods to solve these equations. In this research, the homotopy perturbation method is used for solving an inverse parabolic equation and computing an unknown time-dependent parameter. The homotopy perturbation technique is an analytical procedure for finding the solutions of differential equations which is based on the constructing of a homotopy with an imbedding parameter p∊[0,1] that is considered as an ‘expanding parameter’. In this paper, a very brief introduction to the applications of the used technique and its new development is given. The results of applying this procedure to the studied parabolic inverse problem show the high accuracy, simplicity and efficiency of the approach.