The comparison of different type of systems of odes by using Sumudu and Elzaki transform and Adomian decomposition and Taylor collocation methods

In this thesis, we consider on the solutions of the systems of linear and nonlinear ordinary differential equations with initial conditions by using Sumudu and Elzaki integral transform method,Taylor collocation method and Adomian decomposition method. In the first chapter, Sumudu integral transform method, which is widely used in the field of engineering, is introduced and applied to the system of ordinary differential equations with constant coefficients. After that we found the solutions of the systems of first and second order linear differential equation analytically by using Elzaki integral transform which is recently emerged and very similar to Sumudu integral transform method. In the second chapter, we obtain the approximate and exact solutions of systems of linear and nonlinear ordinary differential equations with variable coefficients by using Taylor collocation method by utilizing Taylor expansions of functions in those differential equations. In the third chapter, we converted linear and nonlinear ordinary differential equations and systems of different orders to the first-order differential equations and found the numerical solutions easily by Adomian decomposition method. As searching for solutions by this method we also expressed that in the systems which contain non-linear terms, it is more easy to process the calculations after decomposing the non-linear terms. In the fourth chapter, we compare exact solutions with the solutions obtained approximately by Taylor collocation method and Adomian decomposition method by making tables.