# Coefficients for the study of Runge-Kutta integration processes

@article{Butcher1963CoefficientsFT, title={Coefficients for the study of Runge-Kutta integration processes}, author={John C. Butcher}, journal={Journal of the Australian Mathematical Society}, year={1963}, volume={3}, pages={185 - 201} }

We consider a set of η first order simultaneous differential equations in the dependent variables y1, y2, …, yn and the independent variable x ⋮ No loss of gernerality results from taking the functions f1, f2, …, fn to be independent of x, for if this were not so an additional dependent variable yn+1, anc be introduced which always equals x and thus satisfies the differential equation

## 383 Citations

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The Runge-Kutta method for integrating an autonomous system of ordinary differential equations, k and m as large as possible, and the number of conditions and variables is given.

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This thesis develops the equations of condition necessary for determining the coefficients for Runge-Kutta methods used in the solution of ordinary differential equations. The equations of condition…

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The condition equations are derived by the introduction of a system of equivalent differential equations, avoiding the usual formalism with trees and elementary differentials. Solutions to the…

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Runge–Kutta (RK)-methods are treated here as linear multistage methods within the author’s concept of A-methods, and it is shown how the order of a RK-method depends on the error constants of its stages.

Order conditions for numerical methods for partitioned ordinary differential equations

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SummaryMotivated by the consideration of Runge-Kutta formulas for partitioned systems, the theory of “P-series” is studied. This theory yields the general structure of the order conditions for…

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to sixth order accuracy. His methods are each eight stage Runge-Kutta processes and differ mainly in that the later process has simpler coefficients occurring in it. In the derivation of the…

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- Computer Science
- 1982

Runge-Kutta methods (RK methods, in short) are popular because of the high accuracy and the feasibility of changing step-size, and in general the methods are expressed as follows.

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