Stable Positive Integral Deferred Correction Methods for Positive Dynamical Systems

Pezzella Mario

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arXiv · 2606.29523

Stable Positive Integral Deferred Correction Methods for Positive Dynamical Systems

Pezzella Mario

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Abstract

In this paper, we introduce the class of Stable Positive Integral Deferred Correction (SPIDeC) methods for the numerical integration of positive dynamical systems. The proposed framework embeds a deferred correction mechanism within an exponential-type Volterra reformulation of the underlying differential problem. The resulting multiplicative structure guarantees the unconditional preservation of both positivity and equilibria, independently of the integration stepsize. Arbitrarily high-order accuracy is systematically achieved through successive explicit-in-sweep corrections applied to a low-order base approximation. From a stability viewpoint, the SPIDeC integrators are L-stable and exactly reproduce the continuous semigroup generated by diagonal linear operators. Furthermore, when Gauss--Radau quadrature nodes are employed, the associated discrete flow asymptotically approaches a logarithmically contractive map as the number of sweeps increases, ensuring stability. Numerical experiments are provided to validate the theoretical analysis and illustrate the practical performance of the proposed methods.

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Pezzella Mario. 2026-06-28. Stable Positive Integral Deferred Correction Methods for Positive Dynamical Systems. https://arxiv.org/abs/2606.29523

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