Multiple-Relaxation Runge Kutta Methods for Conservative Dynamical Systems

by   Abhijit Biswas, et al.
King Abdullah University of Science and Technology

We generalize the idea of relaxation time stepping methods in order to preserve multiple nonlinear conserved quantities of a dynamical system by projecting along directions defined by multiple time stepping algorithms. Similar to the directional projection method of Calvo et. al., we use embedded Runge-Kutta methods to facilitate this in a computationally efficient manner. Proof of the accuracy of the modified RK methods and the existence of valid relaxation parameters are given, under some restrictions. Among other examples, we apply this technique to Implicit-Explicit Runge-Kutta time integration for the Korteweg-de Vries equation and investigate the feasibility and effect of conserving multiple invariants for multi-soliton solutions.


Accurate Solution of the Nonlinear Schrödinger Equation via Conservative Multiple-Relaxation ImEx Methods

The nonlinear Schrödinger (NLS) equation possesses an infinite hierarchy...

General Relaxation Methods for Initial-Value Problems with Application to Multistep Schemes

Recently, an approach known as relaxation has been developed for preserv...

Resolving Entropy Growth from Iterative Methods

We consider entropy conservative and dissipative discretizations of nonl...

A necessary condition for non oscillatory and positivity preserving time-integration schemes

Modified Patankar (MP) schemes are conservative, linear implicit and unc...

Deep projection networks for learning time-homogeneous dynamical systems

We consider the general class of time-homogeneous dynamical systems, bot...

An explicit and practically invariants-preserving method for conservative systems

An explicit numerical strategy that practically preserves invariants is ...

Please sign up or login with your details

Forgot password? Click here to reset