Special Type of Nonlinear Partial Differential Equations - Al-Fayadh, Ali Hassan Nasser;Faraj, Dina Saad
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In this book, two methods are proposed to solve specific types of nonlinear partial differential equations, which are the Sine-Gordon and the Goursat Problem. The first method uses the variation iteration method (VIM) after taking the Laplace transformation which is called Laplace transformation and VIM (LT-VIM). The proposed method is used to solve the Sine-Gordon equation and proven to be very effective compared to existing methods such as the VIM, ADM, HPM, and the RDTM as this method required only one iteration to achieve a value very close to exact solution. Two examples were solved to…mehr

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Produktbeschreibung
In this book, two methods are proposed to solve specific types of nonlinear partial differential equations, which are the Sine-Gordon and the Goursat Problem. The first method uses the variation iteration method (VIM) after taking the Laplace transformation which is called Laplace transformation and VIM (LT-VIM). The proposed method is used to solve the Sine-Gordon equation and proven to be very effective compared to existing methods such as the VIM, ADM, HPM, and the RDTM as this method required only one iteration to achieve a value very close to exact solution. Two examples were solved to approve the method one with approximate solution and the other with exact one. Another problem explored in this book is the Goursat-Problem to achieve the exact solution. The usage of Laplace transform was not the best choice in this case since there will be two variables to deal with. A method called Laplace substitution was shown to be very efficient for getting approximate solutions of manylinear and nonlinear partial differential equations. The Laplace substitution method was combined with VIM to achieve the exact solution of Goursat problem.
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Autorenporträt
Professor wavelet basis function ¿ Applied Mathematics at the Department of Mathematical and Computer Applications / College of Science/ Al-Nahrain University / Iraq, has research published in international, Arab and local magazines, supervised more than 12 Msc. & Ph.D theses in different branches of Applied Mathematics.