带有未知控制参数抛物方程反问题的时空谱方法  

SPACE-TIME SPECTRAL METHOD FOR PARABOLIC INVERSE PROBLEM WITH UNKNOWN CONTROL PARAMETER

作　　者：刘亮[1] 马和平[1] Liu Liang;Ma Heping(College of Sciences,Shanghai University,Shanghai 200444,China)

机构地区：[1]上海大学理学院,上海200444

出　　处：《数值计算与计算机应用》2020年第1期19-26,共8页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(11571224).

摘　　要：对于未知控制参数的抛物方程反问题建立了时空谱方法,在空间方向采用Legendre-Galerkin方法离散,时间方向采用Legendre-tau方法离散,对非线性项采用Chebyshev插值,可使用快速变换计算.使用显隐迭代方法求解离散后的方程,并通过增加的条件来修正控制参数.对于时间区间较大的情况,给出时间方向多区间时空谱方法,可改善迭代收敛性.数值结果验证了该方法的有效性.The space-time spectral method is applied to the parabolic inverse problem with a unknown control parameter.The proposed method is based on Legendre-Galerkin collocation method to discretize in space and Legendre-tau collocation method to discretize in time,and Chebyshev interpolation is used for the non-linear term,which is calculated by fast transformation.For the discretized equation,implicit iteration method is used to solve it,and the control parameter is corrected by the overspecification condition in iteration process.For the non-convergence of iteration caused by large time interval,the multi-interval in time direction method is adopted.Numerical results show the effectiveness of the method.

关 键 词：反问题 控制参数 时空谱方法 

分 类 号：O175.26[理学—数学]