Parallel methods for ODEs with improved absolute stability boundaries (Q1309231)

Explicit PECE multi-block methods are considered for the parallel solution of mildly stiff initial value problems. The general procedure adopted is to consider modifications to existing methods of this type in order to achieve bigger regions of absolute stability. More specifically, from an existing PECE method a new method is derived by taking a linear combination of the predicted and corrected values to define the output values. For a number of well-known methods particular combinations are derived experimentally using computer searches, to get methods with improved stability regions. For comparison purposes the local truncation error terms are also given for all the original and modified formulae considered. Typical cost/accuracy plots are given for all the methods, based on constant stepsize implementations.