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Variational iteration method several studies

Author: ZhangSongSong
Tutor: HanDanFu
School: Zhejiang University
Course: Computational Mathematics
Keywords: Variational iteration method Variational Principle Restricted variation Order integrodifferential equations The second class of integral equations Taylor expansion method
CLC: O241.6
Type: Master's thesis
Year: 2008
Downloads: 184
Quote: 1
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Abstract


This paper discusses the variational iteration method [VIM] and its numerical solution for solving integral equations of the application . Paper is divided into four chapters. The first chapter introduces the numerical solution of the integral equation iterative method and projection method, these methods are proposed to VIM foundation ; subsequently introduced variational method and variational principles related concepts and theorems , which is the theoretical basis of VIM . The second chapter explains the VIM are involved in some of the basic concepts, including the general Lagrange multiplier , stability conditions, limitations VARIATIONALINEQUALITIES facilitate subsequent discussions , but also introduces the basic principles of VIM and its convergence . Chapter III is proposed to solve the second class of integral equations of the variational iteration method . VIM is given by solving Fredholm and Volterra -type integral equation of the specific process , the key is the derivative of both sides of the equation by the number , get fit with VIM form of equations to be solved , then the principle of variational iteration method to construct the corresponding iterative scheme ; Finally, two numerical examples illustrate the effectiveness of the method , and with the literature Taylor expansion method numerical results are compared to prove that our approach has obvious advantages . The fourth chapter discusses the VIM for solving high-order differential equations of Volterra type integral aspects of the application . VIM presents an indirect method , the upcoming high-order equations into equations of the form , then this equation for each construct variational iteration variable format , here we give a detailed construction of iterative process , indicating indirect the VIM method for solving the Lagrange multiplier λ process is simple , and for each function corresponding λ values ​​are -1 , so solving the Lagrange multiplier λ process can be omitted , and the direct cause of λ = -1 to get iterative formula ; final we give two numerical examples , and the results are compared in the literature , show the results obtained indirectly VIM is less than the error results in the literature .

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