### Abstract

The construction of two-step Runge-Kutta methods of order p and stage order q = p with stability polynomial given in advance is described. This polynomial is chosen to have a large interval of absolute stability for explicit methods and to be A-stable and L-stable for implicit methods. After satisfying the order and stage order conditions the remaining free parameters are computed by minimizing the sum of squares of the difference between the stability function of the method and a given polynomial at a sufficiently large number of points in the complex plane.

Original language | English (US) |
---|---|

Pages (from-to) | 51-70 |

Number of pages | 20 |

Journal | Numerical Algorithms |

Volume | 18 |

Issue number | 1 |

State | Published - 1998 |

### Fingerprint

### Keywords

- Least squares minimization
- Stability analysis
- Two-step Runge-Kutta methods

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

*Numerical Algorithms*,

*18*(1), 51-70.

**Construction of two-step Runge-Kutta methods of high order for ordinary differential equations.** / Bartoszewski, Z.; Jackiewicz, Zdzislaw.

Research output: Contribution to journal › Article

*Numerical Algorithms*, vol. 18, no. 1, pp. 51-70.

}

TY - JOUR

T1 - Construction of two-step Runge-Kutta methods of high order for ordinary differential equations

AU - Bartoszewski, Z.

AU - Jackiewicz, Zdzislaw

PY - 1998

Y1 - 1998

N2 - The construction of two-step Runge-Kutta methods of order p and stage order q = p with stability polynomial given in advance is described. This polynomial is chosen to have a large interval of absolute stability for explicit methods and to be A-stable and L-stable for implicit methods. After satisfying the order and stage order conditions the remaining free parameters are computed by minimizing the sum of squares of the difference between the stability function of the method and a given polynomial at a sufficiently large number of points in the complex plane.

AB - The construction of two-step Runge-Kutta methods of order p and stage order q = p with stability polynomial given in advance is described. This polynomial is chosen to have a large interval of absolute stability for explicit methods and to be A-stable and L-stable for implicit methods. After satisfying the order and stage order conditions the remaining free parameters are computed by minimizing the sum of squares of the difference between the stability function of the method and a given polynomial at a sufficiently large number of points in the complex plane.

KW - Least squares minimization

KW - Stability analysis

KW - Two-step Runge-Kutta methods

UR - http://www.scopus.com/inward/record.url?scp=0032344798&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032344798&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032344798

VL - 18

SP - 51

EP - 70

JO - Numerical Algorithms

JF - Numerical Algorithms

SN - 1017-1398

IS - 1

ER -