# Runge–Kutta methods

## Papers overview

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2010

2010

- 2010

The optimum Runge-Kutta method of a particular order is the one whose truncation error is a minimum. Various measures of the size… (More)

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2010

2010

- 2010

The present paper develops a theory of Natural Continuous Extensions (NCEs) for the discrete approximate solution of an ODE given… (More)

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2008

2008

- 2008

We show that while Runge-Kutta methods cannot preserve polynomial invariants in general, they can preserve polynomials that are… (More)

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2007

2007

- Scholarpedia
- 2007

Runge Kutta methods are used to solve ordinary differential equations. Ordinary Differential Equations have a wide application… (More)

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2006

2006

- Applied Mathematics and Computation
- 2006

The present paper continues the research in [H.Y. Liu, G. Sun, Symplectic RK methods and symplectic PRK methods with real… (More)

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2003

Highly Cited

2003

- 2003

Implicit-explicit (IMEX) linear multistep time-discretization schemes for partial differential equations have proved useful in… (More)

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2000

2000

- 2000

Exponentially tted Runge–Kutta methods with s stages are constructed, which exactly integrate di erential initial-value problems… (More)

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1999

Highly Cited

1999

- 1999

We present a family of Runge-Kutta type integration schemes of arbitrarily high order for differential equations evolving on… (More)

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1999

1999

- 1999

A connection between the algebra of rooted trees used in renormalization theory and Runge-Kutta methods is pointed out. Butcher’s… (More)

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1997

1997

- 1997

Apart from speciic methods amenable to speciic problems, symplectic Runge-Kutta methods are necessarily implicit. The aim of this… (More)

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