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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:
65L06Multistep, Runge-Kutta, and extrapolation methods
34A34Nonlinear ODE and systems, general
34C25Periodic solutions of ODE
65L70Error bounds (numerical methods for ODE)
65L50Mesh generation and refinement (ODE)
65L05Initial value problems for ODE (numerical methods)
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References:
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