Special Type of Nonlinear Partial Differential Equations: On Solving Special Type of Nonlinear Partial Differential Equations - Softcover

Al-Fayadh, Ali Hassan Nasser; Faraj, Dina Saad

Softcover

ISBN 10: 6200505365 ISBN 13: 9786200505361

Publisher: LAP LAMBERT Academic Publishing, 2020

Synopsis

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 many linear and nonlinear partial differential equations. The Laplace substitution method was combined with VIM to achieve the exact solution of Goursat problem.

Edition details

• Publisher: LAP LAMBERT Academic Publishing
• Publication date: 2020
• Language: English
• ISBN 10: 6200505365
• ISBN 13: 9786200505361
• Binding: Paperback
• Number of pages: 92