DeepAI AI Chat
Log In Sign Up

Discrete Variational Methods and Symplectic Generalized Additive Runge–Kutta Methods

01/20/2020
by   Antonella Zanna, et al.
University of Bergen
0

We consider a Lagrangian system L(q,q̇) = ∑_l=1^NL^{l}(q,q̇), where the q-variable is treated by a Generalized Additive Runge–Kutta (GARK) method. Applying the technique of discrete variations, we show how to construct symplectic schemes. Assuming the diagonal methods for the GARK given, we present some techinques for constructing the transition matrices. We address the problem of the order of the methods and discuss some semi-separable and separable problems, showing some interesting constructions of methods with non-square coefficient matrices.

READ FULL TEXT

page 1

page 2

page 3

page 4

01/03/2021

Matrix constructs

Matrices can be built and designed by applying procedures from lower ord...
09/24/2019

Symplectic P-stable Additive Runge–Kutta Methods

Symplectic partitioned Runge–Kutta methods can be obtained from a variat...
03/26/2019

Constructions of MDS convolutional codes using superregular matrices

Maximum distance separable convolutional codes are the codes that presen...
06/07/2023

Symplectic multirate generalized additive Runge-Kutta methods for Hamiltonian systems

Generalized additive Runge-Kutta (GARK) schemes have shown to be a suita...
08/30/2013

Separable Approximations and Decomposition Methods for the Augmented Lagrangian

In this paper we study decomposition methods based on separable approxim...
08/04/2021

Explicit RIP matrices: an update

Leveraging recent advances in additive combinatorics, we exhibit explici...
05/30/2023

Methods for Collisions in Some Algebraic Hash Functions

This paper focuses on devising methods for producing collisions in algeb...