Construction of high order diagonally implicit multistage integration methods for ordinary differential equations (Q1294581)

In this paper \(s\)-stage, \(r\)-value diagonally implicit multivalue methods for ordinary differential equations are constructed with stage orders \(p=5\) and \(p=6\) with \(p= r=s\), suitable for either nonstiff or stiff problems. These methods have precisely the same stability properties as the corresponding explicit and diagonally implicit Runge-Kutta methods of the same order. The method parameters are obtained numerically with the aid of nonlinear optimization routines.