A seminumeric approach for solution of the Eikonal partial differential equation and its applications

Authors

  • Mehdi Dehghan,

    Corresponding author
    1. Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran 15914, Iran
    • Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hapez Ave., Tehran 15914, Iran
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  • Rezvan Salehi

    1. Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran 15914, Iran
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Abstract

In this work, a partial differential equation, which has several important applications, is investigated, and some techniques based on semianalytic (or quasi-numerical) approaches are developed to find its solution. In this article, the homotopy perturbation method (HPM), Adomian decomposition method, and the modified homotopy perturbation method are proposed to solve the Eikonal equation. HPM yields solution in convergent series form with easily computable terms, and in some case, yields exact solutions in one iteration. In other hand, in Adomian decomposition method, the approximate solution is considered as an infinite series usually converges to the accurate solution. Moreover, these methods do not require any discretization, linearization, or small perturbation, and therefore reduce the numerical computation a lot. Several test problems are given and results are compared with the variational iteration method. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010

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