A General Study For Some Nonlinear Differential Equations

In this dissertation,we introduce some ideas of variational iteration method and Laplace transformation to find the solution of nonlinear ordinary and partial differential equations.Vari-ational iteration method reveals the approximate solution through the the iterations in the recur-rence relation.Some ordinary and partial differential equations like Legendre ordinary differen-tial equations,K(2,2)and fifth-order KdV are presented to show the validity of this suggested approach.This dissertation comprises of the following topics.In Chapter 1,we outline the background and research status.In Chapter 2,variational iteration method is performed to elucidate the Legendre ordinary differential equations.We apply a substitution which modifies the Legendre ordinary differential equations to a standard ordinary differential equations.Using this substitution,this approach will be very simple and execute the results straight forward.Hence,the excellent results reveal that it is feasible to obtain an analytical or approximate solution of general problems by VIM.Some illustrations are specified,which reduces the calculation and overcomes the hurdle of nonlinear terms to demonstrate the competence of this method.In Chapter 3,The goal of this study deals with an effective approach to achieve the approx-imate solution of nonlinear partial differential equations.This approach exempts the calculation of integration in recurrence relation,and use the convolution theorem in Laplace transforms to compute the value of Lagrange multiplier.This approach demonstrates the high efficiency and attains very good agreement in illustrated problems.