There is no natural parallelism across time in ODEs, so to exploit massive parallelism for a small system of equations it is necessary to use iterative techniques in time, such as waveform. The Picard method, for example, allows each integration to be performed in O(log N) time over N time steps but its convergence is poor for any but almost quadrature problems (∂f∂y small). Generalized Picard, or waveform, may have much faster convergence but less parallelism. This paper considers parallelism across time, explores a proposal made in an earlier paper , and reports on some tests made on that method. © 1993.
Gear, C. W., & Xuhai, X. (1993). Parallelism across time in ODEs. Applied Numerical Mathematics, 11(1–3), 45–68. https://doi.org/10.1016/0168-9274(93)90039-T