A New Analytical Approximate Approach for Non-Linear Initial Value: Problems

Sabah Abdul-Wahab, Mohammed, Jaber Ali Al-Saif, Abdul-Sattar

ISBN 10: 6139454735 / ISBN 13: 9786139454730

Published by LAP LAMBERT Academic Publishing, 2019

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Bibliographic Details

• Title: A New Analytical Approximate Approach for Non-Linear Initial Value: Problems
• Publisher: LAP LAMBERT Academic Publishing
• Publication Date: 2019
• Language: English
• ISBN 10: 6139454735
• ISBN 13: 9786139454730
• Binding: paperback
• Condition: New
• Book Type: book

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Synopsis

This thesis presents a new analytical approximate approach for solving non-linear initial value problems using Taylors' expansion technique. This approach uses derivative components of Taylors' series expansion as a key in its construction. The new approach gave us analytical solutions for some non-linear problems. Naturally, these solutions are in the form of a power series, and its coefficients represent to the nonlinear terms (sometime linear and nonlinear) in the NPDE. The effectiveness of this approach is demonstrated through several examples. These examples are Biological Population model equations, Zakharov–Kuznetsov equations and system of Burger equations. The new approach leaded to significant improvements both in terms of computational time, convergence and accuracy, and the computational results were reinforced by the convergence theorems proofs theoretically. The tables and figures of the new analytical approximate solutions show the validity, usefulness, and importance of the new approach. Moreover, we can consider that this approach is a well-developed mathematical tool to solving non-linear partial differential equations comparing with the other existing methods.