Numerical study for periodical delay differential equations using Runge-Kutta with trigonometric interpolation

A trigonometrically fitted diagonally implicit two-derivative Runge–Kutta method (TFDITDRK) is used for the numerical integration of first-order delay differential equations (DDEs) which possesses oscillatory solutions. Using the trigonometrically fitted property, a three-stage fifth-order diagonally implicit two- derivative Runge–Kutta (DITDRK) method is derived. Here, we employed trigonometric interpolation for the approximation of the delay term. The curves of efficiency based on the log of maximum errors against the log of function evaluations and the CPU time spent to perform the integration are plotted, which then clearly illustrated the superiority of the trigonometrically fitted DITDRK method in comparison with its original method and other existing diagonally implicit Runge–Kutta (DIRK) methods.

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