Browsing by Author "Sinshaw Simachew"

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    Existence and Approximation of Solution of Explicit Second Order Nonlinear Neumann Problems
    (Addis Ababa University, 2015-01) Sinshaw Simachew; Abdi Tadesse (PhD)
    In this paper we shall present the basic theory of Neumann boundary value problem (BVP) together with a discussion of some of the powerful methods that are used to solve the Neumann boundary value problem (NBVP). Especialy the paper focuses on the upper and lower solutions of NBVP. .The main objective of this paper is to investigate the existence and approximation of solutions of second order nonlinear Neuman problems. The paper consists of four main sections: The first section, the introductory part, deals about general introduction and some preliminary considerations. In the second section,the quasilinearization technique, and generalization quasilinearization technique will be deffned and discussed;upper and lower solutions of Neumann BVP and elaborate through examples. And then some basic properties of NBVP (theorems on NBVP) are stated and clari- fied where the proofs of most of these properties are also include. Having familiarized with NBVP in the second section, in the third section,(the core part of the paper), we will come across with Generalized quasilinearization technique