High order methods for irreversible equations
This work provides a new numerical technique for solving irreversible partial differential equations, which is relevant for researchers in computational mathematics and physics.
The authors develop high-order splitting methods that avoid negative steps, enabling numerical integration of irreversible equations such as reaction-diffusion systems. They prove convergence for a broad class of semi-linear problems, including Hamiltonian and reaction-diffusion systems.
In this work, we show high order splitting methods of integration without negative steps, allowing us to solve numerically irreversible problems, like reaction-diffusion equations. The methods consist in a suitable affine combinations of Lie-Trotter schemes with different steps. We prove convergence of this methods for a large class of semi-linear problems, that includes Hamiltonian and reaction-diffusion systems.