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001034860 1001_ $$0P:(DE-Juel1)190575$$aBaumann, Thomas$$b0$$eCorresponding author
001034860 245__ $$aAdaptive time step selection for spectral deferred correction
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001034860 520__ $$aSpectral Deferred Correction (SDC) is an iterative method for the numerical solution of ordinary differential equations. It works by refining the numerical solution for an initial value problem by approximately solving differential equations for the error, and can be interpreted as a preconditioned fixed-point iteration for solving the fully implicit collocation problem. We adopt techniques from embedded Runge-Kutta Methods (RKM) to SDC in order to provide a mechanism for adaptive time step size selection and thus increase computational efficiency of SDC. We propose two SDC-specific estimates of the local error that are generic and do not rely on problem specific quantities. We demonstrate a gain in efficiency over standard SDC with fixed step size and compare efficiency favorably against state-of-the-art adaptive RKM.
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001034860 536__ $$0G:(EU-Grant)955701$$aTIME-X - TIME parallelisation: for eXascale computing and beyond (955701)$$c955701$$fH2020-JTI-EuroHPC-2019-1$$x1
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001034860 7001_ $$00000-0003-0287-2120$$aGötschel, Sebastian$$b1
001034860 7001_ $$00000-0003-1745-0780$$aLunet, Thibaut$$b2
001034860 7001_ $$00000-0003-1904-2473$$aRuprecht, Daniel$$b3
001034860 7001_ $$0P:(DE-Juel1)132268$$aSpeck, Robert$$b4
001034860 773__ $$0PERI:(DE-600)2002650-X$$a10.1007/s11075-024-01964-z$$p369-393$$tNumerical algorithms$$v100$$x1017-1398$$y2025
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