Numerical scheme for the solution of the "bad" Boussinesq equation
Christophe Charlier, Daniel Eriksson, Jonatan Lenells
TL;DR
This paper introduces a numerical method for solving the challenging 'bad' Boussinesq equation, validating its accuracy through comparisons with exact soliton solutions and asymptotic formulas.
Contribution
A new numerical scheme tailored for the 'bad' Boussinesq equation, with validation against known solutions and asymptotic behaviors.
Findings
The scheme accurately reproduces soliton solutions.
The numerical results agree with asymptotic formulas.
The method improves computational stability for this equation.
Abstract
We present a numerical scheme for the solution of the initial-value problem for the ``bad'' Boussinesq equation. The accuracy of the scheme is tested by comparison with exact soliton solutions as well as with recently obtained asymptotic formulas for the solution.
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Taxonomy
TopicsDifferential Equations and Numerical Methods · Numerical methods for differential equations · Advanced Numerical Methods in Computational Mathematics