2011/09/27 by C. Gorria, Gorria, Carlos, Miguel Á. Alejo +3
Mathematics · Physics and Astronomy · #35Q51 #35Q53 #65M06 #65M70 #Differential Equations and Numerical Methods #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1109.6028
openalex publication_date 2011/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Pseudospectral collocation methods and finite difference methods have been\nused for approximating an important family of soliton like solutions of the\nmKdV equation. These solutions present a structural instability which make\ndifficult to approximate their evolution in long time intervals with enough\naccuracy. The standard numerical methods do not guarantee the convergence to\nthe proper solution of the initial value problem and often fail by approaching\nsolutions associated to different initial conditions. In this frame the\nnumerical schemes that preserve the discrete invariants related to some\nconservation laws of this equation produce better results than the methods\nwhich only take care of a high consistency order. Pseudospectral spatial\ndiscretization appear as the most robust of the numerical methods, but finite\ndifference schemes are useful in order to analyze the rule played by the\nconservation of the invariants in the convergence.\n