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العنوان
Approximate Solutions to Some Classes of Nonlinear Partial Differential Equations /
الناشر
Eman Mohamed Mohamed Mohamed,
المؤلف
Mohamed, Eman Mohamed Mohamed.
هيئة الاعداد
باحث / Eman Mohamed Mohamed Mohamed
مشرف / Ibrahim lotfy hassan
مشرف / Hala ahmed el-saka
الموضوع
Mathematics.
تاريخ النشر
2021.
عدد الصفحات
68 p. :
اللغة
الإنجليزية
الدرجة
ماجستير
التخصص
الرياضيات (المتنوعة)
تاريخ الإجازة
1/5/2021
مكان الإجازة
جامعة دمياط - كلية العلوم - الرياضيات
الفهرس
Only 14 pages are availabe for public view

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from 96

Abstract

There are two main goals that we aimed for this thesis. The first is surveying the Adomian decomposition method (ADM) that appears in the literature, which has been explored extensively for attaining analytical or numerical solutions for various linear and nonlinear problems, particularly those that model applications in the physical sciences. The second is introducing an accelerated version of the Adomian decomposition method for solving a class of nonlinear partial differential equations (NPDEs).
This thesis consists of five chapters followed by a list of references. It is organized as follows:
Chapter one. We give a short survey concerning some traditional methods and the recent development methods for solving partial differential equations (PDEs).
Chapter two. We discuss and give a thorough review of the application of the Adomian decomposition method (ADM) on linear and nonlinear ordinary differential equations (ODEs). Also in this chapter, we introduce an accelerated version of Adomian polynomials.
Chapter three. We discuss and apply the decomposition method to linear partial
Differential equations. The main advantage of the method is that it is capable of greatly reducing the size of computational work without affecting the accuracy of the numerical solutions.
Chapter four. The core part of the thesis begins. In this chapter, we focus our study on the nonlinear partial differential equations. We apply the accelerated version of the Adomian decomposition method (ADM) for solving a class of nonlinear partial differential equations (NPDEs). Convergence analysis of this version is discussed and the error of the series solution is estimated. Results of numerical examples show the effectiveness of the proposed technique.
Chapter five. We summarize this dissertation, as well as discuss directions for future research.