Local error control inSDIRK-methods

This paper describes some problems that are encountered in the implementation of a class of Singly Diagonally Implicit Runge-Kutta (SDIRK) methods. The contribution to the local error from the local truncation error and the residual error from the algebraic systems involved are analysed. A section describes a special interpolation formula. This is used as a prediction stage in the iterative solution of the algebraic equations. A strategy for computing a starting stepsize is presented. The techniques are applied to numerical examples.