Auxiliary linear multistep methods: implicit

Abstract

A class of stable implicit 2-step methods of high order for the solution of ordinary differential equations have been developed. The methods use slopes at some auxiliary points within a step. The methods with more number of auxiliary points have shown better stability characteristics. The efficiency of these methods has been established by comparing numerical results with those of 4-step Adams predictor-corrector method and 2-step Butcher's hybrid method.

Keywords:

• Ordinary differential equations
• initial value problems
• multistep methods
• hybrid methods
• numerical algorithms
• zero-stability
• absolute stability
• order and accuracy
• numerical experiments