数学
离散化
积分器
操作员(生物学)
应用数学
指数函数
类型(生物学)
Korteweg–de Vries方程
快速傅里叶变换
反向
数学分析
方案(数学)
傅里叶变换
算法
非线性系统
计算机科学
几何学
生态学
物理
量子力学
生物
计算机网络
生物化学
化学
带宽(计算)
抑制因子
转录因子
基因
作者
Cui Ning,Yifei Wu,Xiaofei Zhao
摘要
In this paper, we propose an embedded low-regularity integrator (ELRI) under a new framework for solving the modified Korteweg-de Vries (mKdV) equation under rough data. Different from the previous work [Wu and Zhao, BIT, Number. Math., (2021)], the present ELRI scheme is constructed based on an approximation of a scaled Schrödinger operator and a new strategy of iterative regularizing through the inverse Miura transform. Moreover, the ELRI scheme is explicitly defined in the physical space, and it is efficient under the Fourier pseudospectral discretization. By rigorous error analysis, we show that ELRI achieves first-order accuracy by requiring the boundedness of one additional spatial derivative of the solution. Numerical results are presented to show the accuracy and efficiency of ELRI.
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