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Block Runge-Kutta methods for the numerical integration of initial value problems in ordinary differential equations. II. The stiff case

J. R. Cash

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Abstract

The approach described in the first part of this paper is extended to include diagonally implicit Runge-Kutta (DIRK) formulae. The algorithms developed are suitable for the numerical integration of stiff differential systems, and their efficiency is illustrated by means of some numerical examples.

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What this paper is about

The approach described in the first part of this paper is extended to include diagonally implicit Runge-Kutta (DIRK) formulae. The algorithms developed are suitable for the numerical integration of stiff differential systems, and their efficiency is illustrated by means of some numerical examples.

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Available abstract

The approach described in the first part of this paper is extended to include diagonally implicit Runge-Kutta (DIRK) formulae. The algorithms developed are suitable for the numerical integration of stiff differential systems, and their efficiency is illustrated by means of some numerical examples.

Key concepts: Runge–Kutta methods, Mathematics, Numerical methods for ordinary differential equations, Backward differentiation formula, Numerical integration, Ordinary differential equation, Explicit and implicit methods, Stiff equation

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Block Runge-Kutta methods for the numerical integration of initial value problems in ordinary differential equations. II. The stiff case — Research Paper | ScholarLens