Adaptive Parareal for Systems of ODEs

摘要: Summary. The parareal scheme (resp. PITA algorithm) proposed in [3] [2]) considers two levels of grids time order to split the domain time-subdomains. A prediction solution is computed on fine grid parallel. Then at each interface between subdomains, makes a jump previous initial boundary value (IBV) next time-subdomain . correction IBV for iteration then coarse time. In this paper, we study adaptivity slice decomposition based an posteriori numerical estimation obtained from step behavior grids. outline paper as follows: section 1, original method recalled and it shown that particular case multiple shooting Deuflhard [1]. 2, definition size fineness slightly modified introduce within algorithm stepping, number decomposition. This leads improvement enables us solve moderately stiff nonlinear ODEs problems. Nevertheless very problems Oregonator model, fails even with introduced adaptivity. develop 3 adaptive parallel extrapolation method, assessment, which obtains results problem.