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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Nonstandard multistep multistage methods are constructed by replacing the timestep with a bounded function, achieving the same convergence order as standard methods while preserving qualitative properties for all positive step sizes.
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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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Some properties of high-order nonstandard multistep multistage methods
Nonstandard multistep multistage methods are constructed by replacing the timestep with a bounded function, achieving the same convergence order as standard methods while preserving qualitative properties for all positive step sizes.