A general [L, M] one-step integrator for initial value problems

Abstract

A general [L≥0, M≥0] one-step integrator is proposed for the solution of the initial value problem in ordinary differential equations. It is general to the extent that the natural numbers L, M, representing the numerator and denominator degrees of the integrator can be selected randomly without any prior knowledge. Sample tests carried out reveal favourable results.

Keywords:

• one-step integrator
• initial value problems
• numerator degree L
• denominator degree M
• convergence and consistency

2010 AMS Subject Classification :

• 65Lxx

Acknowledgements

Dedicated to my beloved, and painstaking postgraduate tutor during my M.Sc studies. Prof G.A. Evans at LUT Loughborough Leicestershire LE 11 3TU, UK (1981–1982).