A 2(3) Pair Pseudo Runge-Kutta Method for Delay Differential Equations

Although explicit pseudo Runge-Kutta methods are less popular than explicit Runge-Kutta methods (because they need two initial values), they are less expensive in terms of functional evaluation. In the past, research has been done in constructing high order pseudo Runge-Kutta methods. In this paper, a low order embedded pair of pseudo Runge-Kutta method will be presented. First, a third order method is constructed by minimizing the error norm follow by constructing a second order method. The stability of the new method is studied. A number of test problems are solved by the new method. The numerical results are shown and compared with the existing method.