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Title: Monotone Iterative Techniques for a Class of Nonlinear Boundary Value Problems
Guide(s): Amit Kumar Verma
Keywords: Monotone Iterative Techniques, Nonlinear Boundary Value Problems
University: Birla Institute of Technology and Science
Completed Date: 1-8-2015
Abstract: This thesis deals with second order nonlinear boundary value problems. We have considered newlineboth continuous as well as discrete boundary value problems. In continuous case, we examine newlineboth analytical and numerical methods, while in discrete case, we discuss analytical results. newlineIn analytical approach, monotone iterative methods are developed for nonlinear three point newlinenonsingular/singular boundary value problems and nonlinear two point discrete boundary newlinevalue problem, respectively. Under the existence of upper and lower solutions, we establish newlinethe analytical results for both cases. In numerical approach, we present two methods and newlinesolve the nonlinear two point singular boundary value problems, which arise in real life. We newlinefocus on variational iteration method (VIM), and homotopy perturbation method (HPM). newlineThis thesis contains twelve chapters. It commences with introduction which is our chapter newline1, then eleven chapters 2 12 and a bibliography section. In chapter 1, we discuss briefly newlineabout boundary value problems and show how the problems get more complicated when we newlinedeal with nonlinear three point boundary value problems. A brief introduction of monotone newlineiterative method with upper and lower solutions are given. Further a survey of literature is newlinegiven to provide a platform required for the forthcoming chapters. In chapters 2 5, nonlinear newlinenonsingular boundary value problems are studied along with mixed type, Neumann type and Dirichlet type boundary conditions. In chapters 6 9, we consider the nonlinear singular boundary value problems with three point boundary conditions. In all cases, we make use newlineof monotone iterative method with the support of upper and lower solutions to establish the existence results. Mostly, we prove existence results for two cases, i.e., when upper and lower solutions follow well order relation or reverse order relation. In chapter 10 and newlinechapter 11, we study the numerical results for nonlinear two point singular boundary value problems by using variational iteration method (VIM) and homotopy
Pagination: 43167 KB
Appears in Departments:Mathematics

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