Singly Implicit Diagonally Extended Runge–Kutta Methods of Fourth Order

摘要

Singly implicit diagonally extended Runge–Kutta methods make it possible to combine the merits of diagonally implicit methods (namely, the simplicity of implementation) and fully implicit ones (high stage order). Due to this combination, they can be very efficient at solving stiff and differ- ential-algebraic problems. In this paper, fourth-order methods with an explicit first stage are exam- ined. The methods have the third or fourth stage order. Consideration is given to an efficient imple- mentation of these methods. The results of tests in which the proposed methods were compared with the fifth-order RADAU IIA method are presented.