On the Rate of Error Growth in Time for Numerical Solutions of Nonlinear Dispersive Wave Equations

02/15/2021
by   Hendrik Ranocha, et al.
0

We study the numerical error in solitary wave solutions of nonlinear dispersive wave equations. A number of existing results for discretizations of solitary wave solutions of particular equations indicate that the error grows quadratically in time for numerical methods that do not conserve energy, but grows only linearly for conservative methods. We provide numerical experiments suggesting that this result extends to a very broad class of equations and numerical methods.

READ FULL TEXT

page 1

page 19

research
06/26/2020

A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations

We develop general tools to construct fully-discrete, conservative numer...
research
10/19/2021

A Numerical Scheme for Wave Turbulence: 3-Wave Kinetic Equations

We introduce a finite volume scheme to solve isotropic 3-wave kinetic eq...
research
02/27/2021

NonlinearSchrodinger: Higher-Order Algorithms and Darboux Transformations for Nonlinear Schrödinger Equations

NonlinearSchrodinger.jl is a Julia package with a simple interface for s...
research
11/15/2021

On the numerical evaluation of the prolate spheroidal wave functions of order zero

We describe a method for the numerical evaluation of the angular prolate...
research
11/15/2021

An 𝒪(1) algorithm for the numerical evaluation of the Sturm-Liouville eigenvalues of the spheroidal wave functions of order zero

In addition to being the eigenfunctions of the restricted Fourier operat...
research
02/03/2018

Numerical verification of the microscopic time reversibility of Newton's equations of motion: Fighting exponential divergence

Numerical solutions to Newton's equations of motion for chaotic self gra...
research
09/14/2020

On the stability and accuracy of the Empirical Interpolation Method and Gravitational Wave Surrogates

The combination of the Reduced Basis (RB) and the Empirical Interpolatio...

Please sign up or login with your details

Forgot password? Click here to reset