Numerical solution of higher order boundary value problem by exp-function method

Abstract

Higher order boundary value problem which are known to arise in the study of astrophysics, hydrodynamic and hydromagnetic stability, fluid dynamics, astronomy, beam and long wave theory, engineering and applied physics. In this thesis under the title “Numerical Solution of Higher Order Boundary Value Problem by Exp-Function Method”, two problems have been studied. Firstly, we discuss the propagation of nonlinear kinky periodic wave and breather wave for the dominant nonlinear pseudo-parabolic physical models: the one-dimensional Oskolkov equation is explored. By executing Exp-Function method, compilation of disguise adaptation of exact nonlinear wave solutions with some noteworthy parameters for the Oskolkov equations is accessed. The presentation of this technique is reliable, direct, and easy to execute contrasted with other existing strategies. Secondly, there are many methods to solve Fisher’s equation, but each method leads to single special solution. In this thesis, a new method, namely the Exp-Function method, is employed to solve the Fisher’s equation. The obtained results are shown graphically. The generalized solution with some free parameters might imply some fascinating meanings hidden in the Fisher’s equation.