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Two time stepping algorithms for parallel computers
Time stepping algorithms are often used to solve parabolic and hyperbolic differential equations numerically. These algorithms are generally regarded as sequential in time; that is, the solution on a time level must be known before the computation of the solution at subsequent time levels can start. While this remains true in principle, we demonstrate that it is possible for processors to perform useful work on many time levels simultaneously. Specifically, it is possible for a processor assigned to a ''later'' time level to compute a very good initial guess for the solution based on approximations to the solutions on ''previous'' time levels, thus reducing the time required for solution. The reduction in the solution time can be measured as parallel speedup. We demonstrate two parallel time stepping algorithms that can be used for both linear and nonlinear problems. We compare the two algorithms and discuss their performance in terms of parameters associated with classical time stepping algorithms. 4 refs., 5 tabs.