Semi-explicit Parareal method based on convergence acceleration technique

摘要: The Parareal algorithm is used to solve time-dependent problems considering multiple solvers that may work in parallel. key feature a initial rough approximation of the solution iteratively refined by parallel solvers. We report derivation method uses convergence acceleration technique improve accuracy solution. Our approach firstly an explicit ODE solver perform computations with different time-steps and then, decomposition into specific convergent series, based on extrapolation method, allows refine precision proposed exploits basic integration methods, such as for example Euler scheme, order preserve simplicity global algorithm. first part paper outlines applied simple scheme then classical discussed illustrated numerical examples.