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

ISBN-13: 9786139454730 / Angielski / Miękka / 2019 / 88 str.

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

Opis

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.

O autorze

Sabah Abdul-Wahab, MohammedMohammed Sabah Abdul-Wahab was born in Basrah city in 1994. He entered the Department of Mathematics in College of Education for Pure Sciences, University of Basrah in 2012. He obtained a bachelor's degree in 2016. He completed his studies in the Department of Mathematics and obtained the master's certificate in 2019 and this book is his thesis.