Numerical-Analytical Evidence of Convergence of the Semi-Discrete Lagrangian-Eulerian Numerical Method for the Korteweg-de Vries Equation
DOI:
https://doi.org/10.5540/03.2026.012.01.0318Palavras-chave:
Extended Lagrangian-Eulerian Approach, Semi-Discrete Method, Korteweg-de Vries Equation, Dispersive Conservation LawResumo
In this work, we present a new extended formulation of the semi-discrete Lagrangian-Eulerian numerical method applied to the Korteweg-de Vries equation, which has a smooth convex flux function. This new scheme is applied to one-dimensional scalar problems incorporating a linear dispersive term with a constant dispersive coefficient. We present here some numerical experiments that provide strong evidence of the method’s convergence. Whenever possible, a comparison is made between the numerical results and exact solutions or highly accurate approximations.
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