New Numerical Methods for Solving Differential Equations

New numerical methods have been developed for solving ordinary differential equations (with and without delay terms). In this approach existing methods such as trapezoidal rule, Adams Moulton methods are improvised using new iterative method (Daftardar-Gejji and Jafari in J Math Anal Appl 316(2):753–763, 2006). Further consistency of the new methods is checked along with error and stability analysis. Numerical examples are presented to illustrate these methods and compared with the existing methods. It is observed that the newly proposed methods yield more accurate results than the existing methods. © 2016, Springer India Pvt. Ltd.