Block Optimized Hybrid Methods for Integrating Singular Second Order Ordinary Differential Equations

Abstract

In this work, a block methods with characteristics of LMF are derived, analyzed and numerically applied to solve singular Initial/Boundary value problems. It was done by applying shift operator to two linear multi-step formula and combined with Optimize hybrid set of formula which are developed at the the first sub-interval to circumvent the singularity at the left end of the integration interval.The mathematical derivation of the proposed methods is based on method of undetermined coefficients where the coefficient in our Linear Multi-step Formulas (LMF) are determined. The fundamental properties of the proposed scheme are analyzed. Finally, the numerical implementation of the method are done on some singular I/B value problem which demonstrate the accuracy and validity of the suggested technique when compared to various strategies available in the current literature.