A Second Derivative Block Method Derived from a Family of Modified Backward Differentiation Formula (BDF) Type for Solving Stiff Ordinary Differential Equations

Abstract

In this work, a second derivative block method derived from a family of modified backward differentiation formula (bdf) type for solving stiff ordinary differential equations has been constructed. Choosing a step number, k = 4, four discrete methods with uniform order 7 are obtained using the multistep collocation approach. The stability properties of the new method have been established. The solutions of two problems have been computed and compared with the corresponding exact and other existing solutions. Solutions are presented on graphs and the associated absolute errors are compared in tables.