Variable step-size techniques in continuous Runge-Kutta methods for isospectral dynamical systems
The authors study the design of a stepsize strategy for a special class of numerical methods for isospectral flows combining a continuous explicit Runge-Kutta method with a Gauss-Legendre Runge-Kutta method. The approach is introduced for double-bracket flows and based on the fact that such a flow can be written as the gradient flow for a potential. The authors show how to compute (approximately) a stepsize such that each step minimizes this potential. Some numerical tests (including an eigenvalue problem for a symmetric matrix) demonstrate the effect of the strategy.
scientific article; zbMATH DE number 1084082
scientific article