Parallel algorithms for solving initial value problems: front broadening and embedded parallelism

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This paper reviews and develops i) broadening of the computation front (BCF) techniques, and ii) block implicit (BI) methods to speed up the numerical solution of IVPS in ODEs by using MIMD computing systems. In particular consideration is given to the performance, accuracy and stability characteristics of the techniques and possible extension of the BCF methods to improve the accuracy. It has been shown that it is not possible to get fourth and higher order parallel explicit Runge-Kutta (RK) methods by using the BCF techniques. This paper also characterizes some of the drawbacks of BCF and considers two further techniques to exploit the parallelism embedded in BI methods.