The non-Newtonian calculi constitute innitely many alternatives to the classical calculus. Among the multiplicative non-Newtonian calculi, the geometric calculus provides a natural framework for problems involving positivity preserving operators. Indeed, some existing positive symplectic schemes for integrating population dynamics can be reinterpreted in the light of the geometric calculus framework. A novel application in the eld of chemical kinetics is proposed. Mass action chemical systems are mass conservative and the solutions are required to remain positive. Hence, numerical methods applied to such kind of equations have to maintain unconditional positivity as well as conservativity in a discrete sense. Composition of geometric Euler scheme with a positive integrator is proposed for integrating production-destruction systems. This work has been supported by GNCS-INDAM.
Positive non-Newtonian integrators for differential systems
A Martiradonna;G Colonna;F Diele
2018
Abstract
The non-Newtonian calculi constitute innitely many alternatives to the classical calculus. Among the multiplicative non-Newtonian calculi, the geometric calculus provides a natural framework for problems involving positivity preserving operators. Indeed, some existing positive symplectic schemes for integrating population dynamics can be reinterpreted in the light of the geometric calculus framework. A novel application in the eld of chemical kinetics is proposed. Mass action chemical systems are mass conservative and the solutions are required to remain positive. Hence, numerical methods applied to such kind of equations have to maintain unconditional positivity as well as conservativity in a discrete sense. Composition of geometric Euler scheme with a positive integrator is proposed for integrating production-destruction systems. This work has been supported by GNCS-INDAM.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
