Application of the numerical methods for KdV equation and inverse strum-liouville problems

In second part of this study, which consist five part, there given basic definitions and theorems of KdV equation and Sturm-Liouville problem.In third part, Adomian Decomposition Method, Homotopy Perturbation Method and Homotopy Analysis Method was applied to KdV equation.In fourth chapter, difference operators was introduced and applied to Sturm-Liouville Problem.In fifth and sixth chapters, different numerical solutions of inverse problems are discussed according to their potential. Differences between potential corresponding to different cores are examined and according to these results it is determined to whether opposite problems are stable or not. Therefore, results of some theorems given by Levitan and Hochtadt for differential cases are given with numerical methods.