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BoltenEtAl2026
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<span id="BoltenEtAl2026">M. Bolten and L. Wimmer, “Spectral deferred corrections parallelized across the method for differential-algebraic equations,” arXiv:2606.25908v1 [math.NA], 2026 [Online]. Available at: <a href="https://arxiv.org/abs/2606.25908v1" target="_blank">https://arxiv.org/abs/2606.25908v1</a></span>
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BibTeX entry <code>BoltenEtAl2026</code>
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<pre class="abstract">@unpublished{BoltenEtAl2026,
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author = {Bolten, Matthias and Wimmer, Lisa},
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howpublished = {arXiv:2606.25908v1 [math.NA]},
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title = {Spectral deferred corrections parallelized across the method for differential-algebraic equations},
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url = {https://arxiv.org/abs/2606.25908v1},
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year = {2026}
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}
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In this work, the performance of different spectral deferred corrections (SDC) methods applied to initial value problems for differential-algebraic equations (DAEs) of index one is analyzed. The SDC method solves a series of correction equations, and after each iteration, the numerical solution is corrected by adding the obtained approximation of the error. The formulation of the SDC method allows for a parallelization across the method to obtain small-scale parallelism, for which a number of processes equal to the number of collocation nodes can be used. Recently, an analytical approach to finding optimal diagonal coefficients for parallel SDC was proposed. So far, no analysis with the new coefficients for parallel SDC applied to DAEs was done. We demonstrate that parallel SDC methods solve DAE problems with high accuracy faster than the associated sequential SDC schemes, obtaining speedup in a small-scale parallel regime.
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GhasemiEtAl2026
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<span id="GhasemiEtAl2026">A. Ghasemi, A. Ghasemi, and J. C. Newman, “Space-Time Discrete Picard Iterations,” <i>International Journal of Applied and Computational Mathematics</i>, vol. 12, no. 4, Jun. 2026, doi: 10.1007/s40819-026-02129-3. [Online]. Available at: <a href="http://dx.doi.org/10.1007/s40819-026-02129-3" target="_blank">http://dx.doi.org/10.1007/s40819-026-02129-3</a></span>
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<pre class="abstract">@article{GhasemiEtAl2026,
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author = {Ghasemi, Arash and Ghasemi, Amirehsan and Newman, James C.},
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doi = {10.1007/s40819-026-02129-3},
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issn = {2199-5796},
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journal = {International Journal of Applied and Computational Mathematics},
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month = jun,
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number = {4},
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publisher = {Springer Science and Business Media LLC},
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title = {Space-Time Discrete Picard Iterations},
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url = {http://dx.doi.org/10.1007/s40819-026-02129-3},
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volume = {12},
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year = {2026}
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