间断初始条件的抛物型方程Crank-Nicolson型外推法的数值色散性分析  

NUMERICAL DISPERSION ANALYSIS OF EXTRAPOLATION OF CRANK-NICOLSON METHOD FOR PARABOLIC EQUATIONS WITH DISCONTINUOUS INITIAL CONDITIONS

作　　者：娜扎开提.阿迪力 伊马木.麦麦提 阿不都热西提.阿不都外力 Nazakat.Adil;Imam.Mamat;Abdurishit.Abduwali(College of Mathematics and System Sciences,Xinjiang University, Urumqi 830046)

机构地区：[1]新疆大学数学与系统科学学院,乌鲁木齐830046

出　　处：《高等学校计算数学学报》2018年第4期297-312,共16页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金资助项目(10971024)

摘　　要：1引言典型的抛物型偏微分方程(如热传导方程)的有限差分方法目前已堪称完善,例如显格式,全隐格式,C-N方法等.前两者对时间变量只有一阶精度,而C-N方法的收敛阶为O(Г^2+h^2),且绝对稳定.但求解间断初始条件的抛物型方程初边值问题时,C-N法却呈现较强的数值色散性效应[1],即在间断附近出现虚假震荡.When the Crank-Nicolson (C-N)method is used to solve the initial- boundary value problem of the parabolic equation with discontinuous initial conditions,if the time step size k and the space step size h are not satisfy the condition that k/h<X/π,then the numerical solution appears spurious oscillation (i.e.numerical dispersion effect).Similarly,the L0-stable C-N extrapolation algorithm is also oscillating when this kind of problem is solved.In the paper,the relationship between the spurious oscillation and the discontinuous initial conditions and the growth factors is mainly studied.The new constraints on the k and the h are given, and the results are generalized to the n-dimensional case.

关 键 词：抛物型方程 色散性 间断 外推法 抛物型偏微分方程 n型 有限差分方法 C-N法 

分 类 号：O241.82[理学—计算数学]