Modified Patankar Linear Multistep methods for production-destruction systems

Abstract

Modified Patankar schemes are linearly implicit time integration methods designed to be unconditionally positive and conservative. In the present work we extend the Patankar-type approach to linear multistep methods and prove that the resulting discretizations retain, with no restrictions on the step size, the positivity of the solution and the linear invariant of the continuous-time system. Moreover, we provide results on arbitrarily high order of convergence and we introduce an embedding technique for the Patankar weight denominators to achieve it.

References in corpus (1)

• An Integro-differential Model of Cadmium Yellow Photodegradation

Cited by in corpus (5)

• High order positivity-preserving numerical methods for a non-local photochemical model
• The Lax-Wendroff theorem for Patankar-type methods applied to hyperbolic conservation laws
• Modified Patankar Semi-Lagrangian Scheme for the Optimal Control of Production-Destruction systems
• An Integro-differential Model of Cadmium Yellow Photodegradation
• A Structure-Preserving Rational Integrator for the Replicator Dynamics on the Probability Simplex