Abstract
This paper will investigate a method to achieve the exact solution of special type of nonlinear partial differential equations (NLPDEs) involving mixed partial derivatives. This proposed method named as Laplace substitution - Variation iteration method (LS-VIM). The method exploits the properties of Laplace substitution method and the Variational iteration method to find the exact solution for Goursat problem involving mixed partial derivatives. In addition, this paper emphasizes the effectiveness of the LS-VIM by solving two examples. The results show that the exact solution can be achieved from a single iteration of the propose method.
Highlights
Nonlinear phenomena have important effects on various fields of applied mathematics and science
Many numerical methods were established for solving the nonlinear type of Goursat problem such as Adomian decomposition method(ADM) [1], Homotopy analysis method(HAM) [9], Variation iteration method (VIM) [10], Two-dimensional differential transform method [8], Modified Variational iteration methods [6], Reduced differential transform method (RDTM) [7] and Finite Difference Method (FDM) [14]
This paper aims to investigate the applicability and the effectiveness of the suggested method to find the exact solution of Goursat nonlinear partial differential equations (NLPDEs)
Summary
Nonlinear phenomena have important effects on various fields of applied mathematics and science. Many numerical methods were established for solving the nonlinear type of Goursat problem such as Adomian decomposition method(ADM) [1], Homotopy analysis method(HAM) [9], Variation iteration method (VIM) [10], Two-dimensional differential transform method [8], Modified Variational iteration methods [6], Reduced differential transform method (RDTM) [7] and Finite Difference Method (FDM) [14]. All these methods have reached the exact solution for solving Goursat problems.
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