求解KdV方程的一种高精确度的数值方法  

A High-Precision Numerical Method for Solving the KdV Equation

作　　者：桑媛 Sang Yuan(Jinzhou Medical University,Jinzhou,Liaoning 121001,China)

机构地区：[1]锦州医科大学,辽宁锦州121001

出　　处：《微型计算机》2025年第4期1-3,共3页

摘　　要：文章提出了KdV方程的一种高精确数值格式,首先采用切比雪夫谱方法分别对一阶、三阶空间导数进行离散,得到一个只与时间相关的常微分方程,再利用求解常微分方程组的四阶指数时间龙格-库塔法构造高精度的数值格式。通过数值实验和比较,验证本文格式的有效性。This paper proposes a high-precision numerical scheme for the KdV equation.Initially,the Chebyshev spectral method is employed to discretize the first and third spatial derivatives,resulting in an ordinary diff erential equation(ODE)that is solely dependent on time.Subsequently,a high-precision numerical scheme is constructed using the fourth-order exponential time Runge-Kutta method,which is designed for solving systems of ODEs.The eff ectiveness of the proposed scheme is verifi ed through numerical experiments and comparisons.

关 键 词：KDV方程 切比雪夫谱方法 四阶指数时间龙格-库塔法 

分 类 号：O17[理学—数学]