Petviashvili type methods for traveling wave computations: I. Analysis of convergence

2013/11/11 by Alvarez, J., Duran, A. · 1 citation
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1311.2546

Abstract

In this paper a family of fixed point algorithms for the numerical resolution of some systems of nonlinear equations is designed and analyzed. The family introduced here generalizes the Petviashvili method and can be applied to the numerical generation of traveling waves in some nonlinear dispersive systems. Conditions for the local convergence are derived and numerical comparisons between different elements of the family are carried out.

Cited by

• Asymptotic-preserving and energy-conserving methods for a hyperbolic approximation of the BBM equation

Related

• On Petviashvili type methods for traveling wave computations: Acceleration techniques
• Numerical generation of periodic traveling wave solutions of some nonlinear dispersive wave equations
• Traveling Wave Solutions for Lotka-Volterra System Re-Visited
• Convergence of Petviashvili's method near periodic waves in the fractional Korteweg-de Vries equation
• On the exact calculation of travelling wave solutions to nonlinear evolution equations