Approximate solutions of singular initial or boundary value problems: Differential transformation and adomian decomposition methods

In this thesis, some special types of initial value and boundary value problems have been solved by differential transformation method and Adomian decomposition method via. In this thesis, most of solved equations were singular initial value and boundary value problems. Solution results of both methods were compared and solution graphics were drawed by composing algorithms.By Differential Transform method, algebraic equations of initial value and boundary value problems are obtained first then tekrar relation is found. Hence, transformation coefficients are calculated in order to obtain approximate solutions or closed form solutions of the problems. It is shown that the approximate solutions are very close or same with analytic solutions when they are compared. Results are shown in appendix by means of table and graphics.By Adomian decomposition method, differential equations are divided into linear and nonlinear parts. Linear y(x) term is decomposed to infinite sum of terms defined as;Also nonlinear F(y(x,t)) term is transformed to decomposition series as,being is Adomian polynoms. Approximate solutions were found by means of Algorithms. Results are shown on appendix with table and graphics.Key words:Differential transform method, Adomian decomposition method ınitial value and boundary value problems, singular initial value and boundary value problems.