Hybrid Linear Multistep Methods with Nested Hybrid Predictors for Solving Linear and Non-linear Initial Value Problems in Ordinary Differential Equations

Abstract

In this paper, we present new class of hybrid linear multistep methods with nested hybrid predictors for the numerical integration of initial value problems in ordinary differential equations. The derivation of the method is based on interpolation and collocation procedures. The region of absolute stability of the new scheme is investigated using the boundary locus method. The method is demonstrated on some linear and non-linear problems; numerical results are tabulated and are compared with some existing methods.

Key words: Interpolation, collocation, nesting, hybrid, predictors, linear multistep methods.