Optimized Runge-Kutta pairs for problems with oscillating solutions

Authors:
Ch. Tsitouras;T. E. Simos
Affiliations:
Department of Applied Mathematics and Physical Sciences, National Technical University of Athens, Zografou Campus 15780, Athens, Greece;Section of Mathematics, Department of Civil Engineering, School of Engineering, University of Thrace, GR-67 100 Xanthi, Greece
Venue:
Journal of Computational and Applied Mathematics
Year:
2002

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Abstract

Three types of methods for integrating periodic initial value problems are presented. These methods are (i) phase-fitted, (ii) zero dissipation (iii) both zero dissipative and phase fitted. Some particular modifications of well-known explicit Runge-Kutta pairs of orders five and four are constructed. Numerical experiments show the efficiency of the new pairs in a wide range of oscillatory problems.