Even though general linear methods were proposed by Professor John Butcher nearly 30 years ago, they have never been thoroughly adopted as practical methods for incorporation into numerical software. The general linear methods are also known as multivalue methods which include the multistep methods and multistage methods as special case. These new methods will have advantages not possessed by either Runge-Kutta methods or by linear multistep methods or other successful known methods. In this talk, we will present some new multivalue methods for solving differential algebraic equations of either index 1 or 2.

These new methods are based on multistep Runge-Kutta methods, one is a 3-stage, 3 step order (4,3) method which is given the diagonal implicit property and so is cheap to implement. We have implemented this method with fixed step size which is very successful. The other is a three stage, 2 step order (3,2) method which works for both fixed and variable step size. Some numerical experiments with these methods are presented.

MINISIMPOSIUM SESSION: 13. Numerical methods for DAEs