Optimized Runge-Kutta pairs for problems with oscillating solutions

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.

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