A Compression Study of Multistep Iterative Methods for Solving Ordinary Differential Equations

Abstract

The objectives of this paper are to introduce the definition of generalized non expansive mapping to analyse the new iterative methods for solving initial value problems (IVPs) of ordinary differential equations (ODEs) and to compare the approximated results by using proposed method. The extended fixed point theorem in complete metric space has been introduced. The convergence analysis of the fixed point method in which generalizes non expansive type mapping in suitable space has been discussed. The numerical solution of the implementation has been studied by comparing the new iterative method with classical methods; Euler, modified Euler and the successive over- relaxation (SOR) methods by using MATLAB. The proposed method has more accuracy and efficiency and less of time complexity than the classical method. The approximated solution is agreeing well with analytical solution for the tested problem.