时间分数阶Burgers方程数值求解的三次B样条配点法  

CUBIC B-SPLINE COLLOCATION METHOD FOR THE NUMERICAL SOLUTION OF TIME FRACTIONAL ORDER BURGERS EQUATIONS

作　　者：张新明 庄博城 Zhang Xinming;Zhuang Bocheng(College of Science,Harbin Institute of Technology(Shenzhen),Shenzhen 518055)

机构地区：[1]哈尔滨工业大学(深圳)理学院,深圳518055

出　　处：《高等学校计算数学学报》2022年第4期311-328,共18页Numerical Mathematics A Journal of Chinese Universities

基　　金：广东省自然科学基金(No.2017A030313280)。

摘　　要：1引言Burgers方程是1948年Burgers[1]首次引入到湍流问题的研究中,它是研究湍流问题的一类重要的非线性偏微分方程,是经典Navier-Stokes方程的简单形式,而且与Hopf-Cole变换导出的热方程密切相关.近些年,随着科学技术和理论的不断发展,分数阶Burgers方程[2]开始日益受到众多专家学者的关注,其相关理论也逐渐被应用于众多物理问题的研究,如:充满粘弹性液体管道中波的传播、粘性介质中的激波、气体的超速传送.In this paper,the solution of the time fractional order Burgers equations is approximated with the cubic B-spline collocation method.The fractional derivative is used in the Caputo sense.To solve these equations,the usual finite difference scheme is used to discretize the time derivative while the approximation of the derivative with respect to space is obtained by the cubic B-spline functions.Thus,the solution of time fractional order Burgers equation can be transformed into the solution of linear equation system,and they can be solved with efficient numerical methods.The convergence order of this scheme is also shown.Two numerical examples are adopted to demonstrate the performance of the proposed scheme.

关 键 词：BURGERS方程 非线性偏微分方程 配点法 热方程 三次B样条 Hopf 粘弹性液体 粘性介质 

分 类 号：O29[理学—应用数学]