Block Runge-Kutta methods for periodic initial-value problems

Abstract

Block Runge-Kutta methods with minimal phase-lag for first order periodic initialvalue problems are developed. It should be noted that the new methods are based on the Runge-Kutta methods of algebraic order three, and on a new error estimate introduced in this paper. The numerical results indicate that these new methods are efficient for the numerical solution of differential equations with periodic solutions, using variable step size.