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Block Runge-Kutta methods for periodic initial-value problems. (English) Zbl 0853.65078
Authors’ abstract: Block Runge-Kutta methods with minimal phase-lag for first-order periodic initial value 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 stepsize.

##### MSC:
 65L06 Multistep, Runge-Kutta, and extrapolation methods 34A34 Nonlinear ODE and systems, general 34C25 Periodic solutions of ODE 65L70 Error bounds (numerical methods for ODE) 65L50 Mesh generation and refinement (ODE) 65L05 Initial value problems for ODE (numerical methods)
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##### References:
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