Numerical Solution to Singular Boundary Value Problems (SBVPS) using Modified Linear Multistep Formulas (LMF)

Abstract

In this work, two block methods with characteristics of LMF are derived, analysed and numerically applied to solve second-order Singular Boundary Problems (SBVPs) of ordinary differential equations. The mathematical derivation of the proposed methods is based on the interpolation and collocation of the exact solution and its derivatives at some selected equidistant grid and off-grid points. The proposed strategy consists in a block method where the collocation at the initial point is avoided to circumvent the singularity at the starting end of the solution interval. The convergence analysis of the discrete solutions of the methods are examined. Finally, some second-order SVBPs of ordinary differential equations are numerically solved to demonstrate the efficiency and validity of the suggested technique, which is compared to various strategies available in the current literature. The result supports the good performance of the derived schemes.