解抛物型方程的Galerkin多层修正迭代算法  

GALERKIN MULTILEVEL MODIFICATION ALGORITHMS FOR PARABOLIC DIFFERENTIAL EQUATIONS

作　　者：何崇南[1] 邓小炎[1] 

机构地区：[1]中山大学科学计算与计算机应用系

出　　处：《数值计算与计算机应用》2008年第2期96-104,共9页Journal on Numerical Methods and Computer Applications

基　　金：广东省自然科学基金(5003308).

摘　　要：小波方法在微分方程数值解法中日益得到广泛应用.由于小波的紧支性、正交性使得离散后的代数方程组的系数矩阵具有稀疏性、层次性,在此基础上可以构造各种快速算法.基于多尺度空间,采用一组正交小波基来离散原方程,导出方程组的系数矩阵具有稀疏性和层次性,从而提出求抛物型微分方程的Galerkin多层修正迭代算法,并讨论了迭代修正算法的收敛性.提出的方案能容易地实现时间和空间方向的局部加密自适应修正过程.提供的数值算例说明了方法的有效性.The wavelets have been widely used in tions. The properties of the wavelets basis the numerical methods of the differential equasuch as orthogonality, compact support lead to the sparseness and multiscale structurre of the coefficient matrix of the linear system. The multiscale orthogonal wavelet base is chosen to discretize the parabolic equations. Due to the sparseness and multiscale structurre of the coefficient matrix of the linear system, a Galerkin multilevel modification iteration algorithm for solving parabolic differential equations is proposed. The convergence properties of the proposed algorithm are discussed. With the methods proposed in this paper, a adaptive local refinement modifying algorithm for time and space can be obtained easily. The numerical example indicates the effectiveness of the proposed algorithm.

关 键 词：抛物型方程 GALERKIN方法 迭代法 自适应方法 

分 类 号：O175.26[理学—数学] TM15[理学—基础数学]