Analysis of nonquadratic energy-conservative schemes for KdV type-equations

Fuente: arXiv
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Main Authors: Kawai, Shuto, Sato, Shun, Matsuo, Takayasu
Format: Preprint
Published: 2024
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_version_ 1866912162969026560
author Kawai, Shuto
Sato, Shun
Matsuo, Takayasu
author_facet Kawai, Shuto
Sato, Shun
Matsuo, Takayasu
contents Numerical schemes that conserve invariants have demonstrated superior performance in various contexts, and several unified methods have been developed for constructing such schemes. However, the mathematical properties of these schemes remain poorly understood, except in norm-preserving cases. This study introduces a novel analytical framework applicable to general energy-preserving schemes. The proposed framework is applied to Korteweg-de Vries (KdV)-type equations, establishing global existence and convergence estimates for the numerical solutions.
format Preprint
id arxiv_https___arxiv_org_abs_2412_15556
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Analysis of nonquadratic energy-conservative schemes for KdV type-equations
Kawai, Shuto
Sato, Shun
Matsuo, Takayasu
Numerical Analysis
65M12
Numerical schemes that conserve invariants have demonstrated superior performance in various contexts, and several unified methods have been developed for constructing such schemes. However, the mathematical properties of these schemes remain poorly understood, except in norm-preserving cases. This study introduces a novel analytical framework applicable to general energy-preserving schemes. The proposed framework is applied to Korteweg-de Vries (KdV)-type equations, establishing global existence and convergence estimates for the numerical solutions.
title Analysis of nonquadratic energy-conservative schemes for KdV type-equations
topic Numerical Analysis
65M12
url https://arxiv.org/abs/2412.15556