SPIDeC methods achieve arbitrarily high-order accuracy for positive dynamical systems while unconditionally preserving positivity and equilibria via a multiplicative Volterra structure, and they are L-stable with asymptotic logarithmic contractivity under Gauss-Radau nodes.
Parallelizing spectral deferred corrections across the method
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Parallel SDC with optimal coefficients solves index-1 DAEs faster than sequential SDC while retaining high accuracy in small-scale parallelism.
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Stable Positive Integral Deferred Correction Methods for Positive Dynamical Systems
SPIDeC methods achieve arbitrarily high-order accuracy for positive dynamical systems while unconditionally preserving positivity and equilibria via a multiplicative Volterra structure, and they are L-stable with asymptotic logarithmic contractivity under Gauss-Radau nodes.
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Spectral deferred corrections parallelized across the method for differential-algebraic equations
Parallel SDC with optimal coefficients solves index-1 DAEs faster than sequential SDC while retaining high accuracy in small-scale parallelism.