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1989•International Journal of Computer MathematicsRequires access

Auxiliary linear multistep methods: implicit

G. Sahoo, Nilanjan Datta

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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.

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What this paper is about

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.

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Available 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.

Key concepts: Linear multistep method, Numerical methods for ordinary differential equations, Mathematics, Backward differentiation formula, Runge–Kutta methods, Ordinary differential equation, Predictor–corrector method, Explicit and implicit methods

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