求解非线性时滞双曲型偏微分方程的紧致差分方法及Richardson外推算法  

A COMPACT DIFFERENCE SCHEME AND RICHARDSON EXTRAPOLATION ALGORITHM FOR SOLVING A CLASS OF THE NONLINEAR DELAY HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS

作　　者：张启峰[1] 张诚坚[1] 邓定文[2] 

机构地区：[1]华中科技大学数学与统计学院,武汉430074 [2]南昌航空大学数学与信息科学学院,南昌330063

出　　处：《数值计算与计算机应用》2013年第3期167-176,共10页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金资助项目(11171125);国家自然科学基金重大研究计划重点项目(9113000);湖北省自然科学基金资助项目(2011CDB289);国家留学基金项目(201306160037)

摘　　要：本文构造了一类求解非线性时滞双曲型偏微分方程的紧致差分格式,获得了该差分格式的唯一可解性,收敛性和无条件稳定性,收敛阶为O(Γ~2+h^4),并进一步对时间方向进行Richardson外推,使得收敛阶达到了O(Γ~4+h^4).数值实验表明了算法的精度和有效性.In this paper, a class of compact difference schemes are constructed to solve the nonlin- ear delay hyperbolic partial differential equations. The unique solvability, convergence and unconditional stability of the scheme are obtained. The convergence order is O（T2-h4）. Furthermore, the Richardson extrapolation is applied to improve the temporal accuracy of the scheme, and a solution of order four in both temporal and spatial dimensions is obtained. Numerical example shows the accuracy and efficiency of the algorithms.

关 键 词：紧致差分格式 唯一性 稳定性 收敛性 RICHARDSON外推 

分 类 号：O241.82[理学—计算数学]