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Theoretically optimal inexact SDC methods

Please always quote using this URN: urn:nbn:de:0297-zib-53140
  • In several inital value problems with particularly expensive right hand side computation, there is a trade-off between accuracy and computational effort in evaluating the right hand sides. We consider inexact spectral deferred correction (SDC) methods for solving such non-stiff initial value problems. SDC methods are interpreted as fixed point iterations and, due to their corrective iterative nature, allow to exploit the accuracy-work-tradeoff for a reduction of the total computational effort. On one hand we derive an error model bounding the total error in terms of the right hand side evaluation errors. On the other hand, we define work models describing the computational effort in terms of the evaluation accuracy. Combining both, a theoretically optimal tolerance selection is worked out by minimizing the total work subject to achieving the requested tolerance.

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Author:Martin WeiserORCiD, Sunayana Ghosh
Document Type:ZIB-Report
Tag:Spectral deferred correction, initial value problems, error propagation, adaptive control of tolerances
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L05 Initial value problems
65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L20 Stability and convergence of numerical methods
65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L70 Error bounds
65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M70 Spectral, collocation and related methods
Date of first Publication:2016/10/27
Series (Serial Number):ZIB-Report (16-52)
Published in:Communications in Applied Mathematics and Computational Science 13, 53-86, 2018. DOI 10.2140/camcos.2018.13.53