Analysis of nonquadratic energy-conservative schemes for KdV type-equations
Numerical Analysis
2024-12-23 v1 Numerical Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.2412.15556,
title = {Analysis of nonquadratic energy-conservative schemes for KdV type-equations},
author = {Shuto Kawai and Shun Sato and Takayasu Matsuo},
journal= {arXiv preprint arXiv:2412.15556},
year = {2024}
}