Embedded Diagonally Implicit Runge-Kutta methods of different orders are used for the treatment of delay differential equations. The delay argument is approximated using an appropriate Hermite Interpolation. The numerical results based on these methods are compared and the Q-stability region of the methods are presented.
In this paper, third-order 3-stage diagonally implicit Runge–Kutta–Nystrom method embedded in fourth-order 4-stage for solving special second-order initial value problems is constructed. The method has the property of minimized local truncation error as well as the last row of the coefficient matrix is equal to the vector output. The stability of the method… (More)