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Rational Runge-Kutta methods for solving systems of ordinary differential equations

Rationale Runge-Kutta Methoden für systeme gewöhnlicher Differentialgleichungen

Abstract

Some nonlinear methods for solving single ordinary differiential equations are generalized to solve systems of equations. To perform this, a new vector product, compatible with the Samelson inverse of a vector, is defined. Conditions for a given order are derived.

Zusammenfassung

Einige nichtlineare Methoden zur numerischen Lösung skalarer gewöhnlicher Differentialgleichungen werden für Systeme verallgemeinert. Zu diesem Zweck wird ein mit den Samelson-Inversen eines Vektors kompatibles Vektorprodukt definiert. Die Bedingungen für einer vorgegebene Ordnung werden hergeleitet.

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Wambecq, A. Rational Runge-Kutta methods for solving systems of ordinary differential equations. Computing 20, 333–342 (1978). https://doi.org/10.1007/BF02252381

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Keywords

  • Differential Equation
  • Ordinary Differential Equation
  • Computational Mathematic
  • Vector Product
  • Nonlinear Method