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A parareal approach of semi‐linear parabolic equations based on general waveform relaxation

The results show that the algorithm for initial‐boundary value problem is superlinearly convergent while both algorithms for the time‐periodic boundary value problem linearly converge to the exact solutions at most.
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The study of parareal algorithm for the linear switched systems

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Analysis of the parareal approach based on discontinuous Galerkin method for time‐dependent Stokes equations

The proposed parareal DG algorithm is proved to be unconditionally stable and bounded by the error of discontinuous Galerkin discretization after a finite number of iterations.
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A fully discrete two-grid method for the diffusive Peterlin viscoelastic model

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Analysis of the parareal algorithm for linear parametric differential equations

This paper presents a parareal algorithm with parameterized propagators for linear parametric differential equations over a wide range of parameters. Through transforming the initial value problem…
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