Diagonally implicit and singly implicit methods for stiff problems

In the numerical solution of stiff ordinary differential equation systems there are conflicting aims of accuracy, stability and low implementation costs. One approach to finding efficient methods is the use of diagonally implicit Runge-Kutta methods, where the cost is comparable to sequential use of BDF-like methods. However, these have disadvantages which can be partly overcome bu the use of singly implicit methods. These in turn lead to some new and promising general linear methods whose stability properties are the same as for Runge-Kutta methods.