K-Step Block Predictor-Corrector Methods for Solving First Order Ordinary Differential Equations

摘要

A k-step block Predictor-Corrector Methods for solving first Order Ordinary Differential Equations (ODEs) are formulated and applied on non-stiff and mildly stiff problems using variable step size technique. In this method, collocation and interpolation of the power series as the approximate solution is carried out with aim of generating the continuous scheme. The investigation of some selected theoretical properties of the method is analyzed as well as determination of the region of absolute stability of the method. In addition, the implementation of the proposed method is done by applying variable step size technique.