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

Z. Bartoszewski, Zdzislaw Jackiewicz

Research output: Contribution to journalArticle

27 Citations (Scopus)

### 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) 51-70 20 Numerical Algorithms 18 1 Published - 1998

### Fingerprint

Two-step Runge-Kutta Methods
Runge Kutta methods
Ordinary differential equations
Ordinary differential equation
Polynomials
Higher Order
Polynomial
Absolute Stability
Order Conditions
Explicit Methods
Implicit Method
Sum of squares
Argand diagram
Interval

### Keywords

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

### ASJC Scopus subject areas

• Applied Mathematics

### Cite this

In: Numerical Algorithms, Vol. 18, No. 1, 1998, p. 51-70.

Research output: Contribution to journalArticle

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