Numerical Methods for Solving Differential Equations

Abstract: In this paper, we introduce a new numerical method for solving ordinary differential equations in both linear and non linear cases. We apply new iterative method (NIM) on implicit midpoint rule to derive a new numerical method. We further present the error, convergence and stability analysis of the proposed method. The efficiency of the new method is tested through various types of numerical problems and it shows that the results are be the same as with exact solutions.