Energy Stability of Explicit Runge-Kutta Methods for Non-autonomous or Nonlinear Problems

09/29/2019
by   Hendrik Ranocha, et al.
0

Many important initial value problems have the property that energy is non-increasing in time. Energy stable methods, also referred to as strongly stable methods, guarantee the same property discretely. We investigate requirements for conditional energy stability of explicit Runge-Kutta methods for nonlinear or non-autonomous problems. We provide both necessary and sufficient conditions for energy stability over these classes of problems. Examples of conditionally energy stable schemes are constructed and an example is given in which unconditional energy stability is obtained with an explicit scheme.

READ FULL TEXT

Authors

page 1

page 2

page 3

page 4

01/24/2021

Towards Stable Radial Basis Function Methods for Linear Advection Problems

In this work, we investigate (energy) stability of global radial basis f...
05/25/2022

Diagonally implicit Runge-Kutta schemes: Discrete energy-balance laws and compactness properties

We study diagonally implicit Runge-Kutta (DIRK) schemes when applied to ...
04/19/2018

NAIS-Net: Stable Deep Networks from Non-Autonomous Differential Equations

This paper introduces "Non-Autonomous Input-Output Stable Network" (NAIS...
11/27/2019

A stability property for a mono-dimensional three velocities scheme with relative velocity

In this contribution, we study a stability notion for a fundamental line...
09/02/2018

Stable approximation schemes for optimal filters

We explore a general truncation scheme for the approximation of (possibl...
06/28/2021

Seeking Stability by being Lazy and Shallow

Designing a language feature often requires a choice between several, si...
03/29/2022

An extended range of energy stable flux reconstruction methods on triangles

We present an extended range of stable flux reconstruction (FR) methods ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.