二阶高振荡边值问题的数值方法  

Numerical Methods for Solving Second Order Highly Oscillatory Boundary Value Problems

作　　者：夏颖双 高旸 耿发展[1] XIA Yingshuang;GAO Yang;GENG Fazhan(School of Mathematics and Statistics,Changshu Institute of Technology,Changshu 215500,China)

机构地区：[1]常熟理工学院数学与统计学院,江苏常熟215500

出　　处：《常熟理工学院学报》2021年第2期103-106,共4页Journal of Changshu Institute of Technology

基　　金：国家自然科学基金项目“基于再生核理论求解奇异摄动边值问题”(11801044);“基于核函数求解变分数阶和分布阶扩散方程”(11271100)。

摘　　要：高振荡微分方程在电路模拟、图像分析、分子动力学和工程等领域有着重要的应用.近几十年来,高振动问题数值格式的分析与设计受到了广泛的关注.结合常数变易公式与再生核函数近似,本文提出一类新的数值方法用于求解具有高振荡解的二阶边值问题.数值实验表明,该方法能够保持解的振荡结构,具有较高的精度.Highly oscillatory differential equations have significant applications in several fields such as circuit simulation,image analysis,molecular dynamics and engineering.The analysis and design of numerical schemes for highly oscillatory problems have received much attention in recent decades.The aim of this paper is to propose a new class of reproducing kernel function-based methods for solving second-order boundary value problems with highly oscillatory solutions.These new methods combine the variation-of-constants formula with the reproducing kernel function approximation.The main advantage of our new methods is that it can preserve the oscillatory structure of the solution to the underlying highly oscillatory systems.The numerical experiments are implemented and the numerical results demonstrate a remarkable accuracy and efficiency of our new methods.

关 键 词：再生核函数 高振荡 边值问题 

分 类 号：O175[理学—数学]