Document Details

Document Type : Thesis 
Document Title :
Adomian Decomposition Method for Solving
طريقة أدومين للتجزئة لحل مسائل القيم الحدية لصنف من المعادلات التفاضلية الجزئية
 
Subject : Adomian Decomposition Method for Solving 
Document Language : Arabic 
Abstract : Abstract The Adomian decomposition method (ADM) is a method for solving nonlinear differential equations. The method was developed by George Adomian in the last twenty years. This method has many important applications especially in the fields of physics, chemistry, mechanics and other sciences. This study seeks to provide an illustration of how the method can be applied on the PDEs and on the Systems of PDEs. Moreover, this study offers an account of the modifications and development of this method since its inception till today, making it a basic building block that can serve any researcher in this field. In addition, the thesis discusses the Goursat's problem for linear and nonlinear hyperbolic equations of the second order. Also, it outlines the Goursat's problem for system of nonlinear hyperbolic equations of the second order as well as the Goursat's problem for linear and nonlinear hyperbolic equations of fourth order. The study also looks at the existence and uniqueness for the initial-Neumann boundary value problems for parabolic, hyperbolic equations and parabolic–hyperbolic equations in Hilbert space. The study describes a new iterative method similar to the Adomian decomposition method for the application of ADM in which initial conditions and boundary conditions (Dirichlet, Neumann and Mixed) are used to find a solution to the Initial- boundary value problems for parabolic, hyperbolic equations and parabolic–hyperbolic equations. Finally, the initial-boundary value problems for the parabolic, hyperbolic equations and parabolic–hyperbolic equations with integral boundary condition were solved by introducing a new function that transforms integral condition to a normal condition, then applying a new method taking into account all the initial and boundary conditions together in ADM with a new differential operator to arrive at solution. Moreover, the thesis has supported by various examples. 
Supervisor : Dr. Lazhar Aboubaker Bougoffa 
Thesis Type : Doctorate Thesis 
Publishing Year : 1434 AH
2013 AD 
Added Date : Sunday, January 4, 2015 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
مريم حويمد المزموميal-Mazmumy, MARIAM HowimedInvestigatorDoctorate 

Files

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 37756.pdf pdf 
 37757.pdf pdf 

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