数学
索波列夫空间
初值问题
Korteweg–de Vries方程
趋同(经济学)
收敛速度
订单(交换)
数学分析
空格(标点符号)
期限(时间)
数学物理
应用数学
物理
非线性系统
钥匙(锁)
生态学
语言学
哲学
财务
量子力学
经济
生物
经济增长
作者
Clémentine Courtès,Frédéric Lagoutìère,Frédéric Rousset
出处
期刊:Cornell University - arXiv
日期:2017-12-06
标识
DOI:10.48550/arxiv.1712.02291
摘要
This article deals with the numerical analysis of the Cauchy problem for the Korteweg-de Vries equation with a finite difference scheme. We consider the Rusanov scheme for the hyperbolic flux term and a 4-points $\theta$-scheme for the dispersive term. We prove the convergence under a hyperbolic Courant-Friedrichs-Lewy condition when $\theta\geq \frac{1}{2}$ and under an "Airy" Courant-Friedrichs-Lewy condition when $\theta<\frac{1}{2}$. More precisely, we get the first order convergence rate for strong solutions in the Sobolev space $H^s(\mathbb{R})$, $s \geq 6$ and extend this result to the non-smooth case for initial data in $H^s(\mathbb{R})$, with $s\geq \frac{3}{4}$ , to the price of a loss in the convergence order. Numerical simulations indicate that the orders of convergence may be optimal when $s\geq3$.
科研通智能强力驱动
Strongly Powered by AbleSci AI