caa a22 4500 467939225 CHVBK 20180406153007.0 cr unu---uuuuu 170328e20060101xx s 000 0 eng 10.1007/s10444-004-4092-6 doi (NATIONALLICENCE)springer-10.1007/s10444-004-4092-6 Multilevel augmentation methods for differential equations [Elektronische Daten] [Zhongying Chen, Bin Wu, Yuesheng Xu] We develop multilevel augmentation methods for solving differential equations. We first establish a theoretical framework for convergence analysis of the boundary value problems of differential equations, and then construct multiscale orthonormal bases in H0m(0,1) spaces. Finally, the multilevel augmentation methods in conjunction with the multiscale orthonormal bases are applied to two-point boundary value problems of both second-order and fourth-order differential equations. Theoretical analysis and numerical tests show that these methods are computationally stable, efficient and accurate. Springer, 2006 multilevel augmentation methods nationallicence multiscale orthonormal bases in Sobolev spaces nationallicence differential equations nationallicence Chen Zhongying Department of Scientific Computing and Computer Applications, Zhongshan University, 510275, Guangzhou, P. R. China aut Wu Bin Department of Scientific Computing and Computer Applications, Zhongshan University, 510275, Guangzhou, P. R. China aut Xu Yuesheng Department of Mathematics, Syracuse University, Syracuse, New York 13244-1150, USA and Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, 100080, Beijing, P. R. China aut Advances in Computational Mathematics Kluwer Academic Publishers 24/1-4(2006-01-01), 213-238 1019-7168 24:1-4<213 2006 24 10444 https://doi.org/10.1007/s10444-004-4092-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10444-004-4092-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chen Zhongying Department of Scientific Computing and Computer Applications, Zhongshan University, 510275, Guangzhou, P. R. China aut NATIONALLICENCE 700 1- Wu Bin Department of Scientific Computing and Computer Applications, Zhongshan University, 510275, Guangzhou, P. R. China aut NATIONALLICENCE 700 1- Xu Yuesheng Department of Mathematics, Syracuse University, Syracuse, New York 13244-1150, USA and Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, 100080, Beijing, P. R. China aut NATIONALLICENCE 773 0- Advances in Computational Mathematics Kluwer Academic Publishers 24/1-4(2006-01-01), 213-238 1019-7168 24:1-4<213 2006 24 10444 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer