Solutions of some non-linear partial differential equations with finite difference method

This thesis consists of three chapters.In the first chapter, provides fundamental definitions related to differential equations.In the second chapter, we give general structures of Finite Difference Method, Adomian Decomposition Method and Homotopy Perturbation Method.The third chapter is the our major contribution and it has two section. In the first section of third chapter, numerical solitions of the KdV equation were investigated by applying Finite Difference Method, ADM and HPM methods respectively to the KdV equation. In the second section of third chapter, numerical solitions of the Burgers equation were investigated by applying Finite Difference Method, ADM and HPM methods respectively to the Burgers equation.Key Words: KdV equation, Burgers equation, Finite Difference Method (SFM),Adomian Decomposition Method (ADM), Homotopy PerturbationMethod (HPM), Crank Nicolson, Adomian Polinomials, Finite Dif-ference Approximation.