Abstract

In this work, we consider two‐derivative Runge‐Kutta methods for the numerical integration of first‐order differential equations with oscillatory solution. We construct methods with constant coefficients and special properties as minimum phase‐lag and amplification errors with three and four stages. All methods constructed have fifth algebraic order. We also present methods with variable coefficients with zero phase‐lag and amplification errors. In order to examine the efficiency of the new methods, we use four well‐known oscillatory test problems.

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