Pad'e Sumudu Adomian Decomposition Method For Solving Nonlinear Schrodinger Equations And KdV-Burger's Equations

The main purpose of this thesis is to study some important linear and nonlinear problems using some suitable analytical and numerical methods such as Sumudu transform,Adomian Decomposition Method(ADM),and Pade approximations technique.The Sumudu transform method can only solve linear PDE.In many literatures we can see the Sumudu Adomian decomposition method(SADM)who is combin-tion of Sumudu transform and Adomian decomposition method,the method is applying to solve nonlinear PDE,but the solution have small convergence radius and the truncated series is inaccurate in many regions for some PDE.We will perfom the SADM solution by using the function P[L/M][·]called double Pade ap-proximation.Then we obtain the convergence domain of PSADM solution larger than SADM solution.In our proposed technic the nonlinear terms are computed using Adomian polynomials,and the Pade approximation will be used to control the convergence of the series solutions.We begin with basic defintions,theorems,and properties in the background materials.We will provide a comprehensive backgroung of the suggested numeri-cal methods.The suggested technique will be use to find the numerical solutions for some well-known problems in science and engineering such as the linear and nonlinear Schrodinger equations,the linear Klein-Gordon equations,and non-linear Burgers equations,and so on.In application,we will provide the basic mathematical formulation of the basic idea of the method,and the absolute er-ror to illustrate the efficiency and the high accuracy of the method.Besides,the graphical numerical simulations in 3D surface solutions of each application is given.The proposed method provide us a suitable way for controlling the conver-gences of series solutions with high accuracy by using different order of Pade approximation.To obtain the best PSADM solution,we provide some conditions which can help to choose the type of the Pade approximation according to the topology of the exact solution u(x,t)and the topology of the SADM solution u(x,t,j).The suggested technique is successfully applied to nonlinear Schrodinger equa-tions,and KdV Burgers equations.The result obtained using PSADM proved to be highly efficient compared to the traditional SADM.