Optimal Runge – Kutta Methods for First Order Pseudospectral Operators

@inproceedings{Mead1999OptimalR,
title={Optimal Runge – Kutta Methods for First Order Pseudospectral Operators},
author={Jodi L. Mead and Rosemary A. Renaut},
year={1999}
}

New Runge–Kutta methods for method of lines solution of systems of ordinary differential equations arising from discretizations of spatial derivatives in hyperbolic equations, by Chebyshev or modified Chebyshev methods, are introduced. These Runge–Kutta methods optimize the time step necessary for stable solutions, while holding dispersion and dissipation fixed. It is found that maximizing dispersion minimizes dissipation, and vice versa. Optimal methods with respect to large stability… CONTINUE READING