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Analysis of the parareal time-parallel time-integration method. (English) Zbl 1141.65064
The parareal method is an algorithm for the parallel solution of time-dependent differential equations. It is based on splitting the complete time interval into small parts and then solving the differential equation on all parts simultaneously in a parallel fashion. A subsequent iteration procedure is then used to assert a continuous transition from each individual part of the solution to its neighbours.
The authors show the relations between this approach and various other well known ideas. This is followed by a convergence analysis that shows superlinear convergence on bounded time intervals and linear convergence on unbounded time intervals.

MSC:
65L20 Stability and convergence of numerical methods for ordinary differential equations
65Y05 Parallel numerical computation
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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