Block Methods for Solving Second Order Ordinary Differential Equation Using Shifted Linear Multistep Formulas

In this paper, a new block numerical integrator with characteristics of linear multi-step formulas (LMFs) is derived, analyzed, and numerically applied to solve second-order ordinary differential equations (ODEs). It was done by applying a shift operator to two linear multi-step formulae with low Local Truncation Error (LTE). The mathematical derivation of the Linear Multi-step Formulas (LMF) used in the method is based on the method of undetermined coefficients. The analysis of the basic properties of the method shows that the scheme is consistent, convergent, and zero stable. The Numerical experimentation and comparative analysis with existing methods show that our scheme is efficient.