Effective computation of optimal stability polynomials. (English) Zbl 1168.65367

Bogatyrëv, Andrei

Calcolo 41, No. 4, 247-256 (2004).

Summary: The construction of stable explicit multistage Runge-Kutta methods during 1950–1960 stumbled over a certain extremal problem for polynomials. The solution to this problem is known as the optimal stability polynomial and its computation is notoriously difficult. We propose a new method for the effective evaluation of optimal stability polynomials which is based on the explicit analytical representation of the solution. The main feature of the method is its independence from the computational complexity of the degree of the solution.

MSC:

65L06	Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
41A10	Approximation by polynomials