@Article{NMTMA-14-461, author = {Zhang , YangYu , Xuhong and Wang , Zhongqing}, title = {Efficient and Accurate Legendre Spectral Element Methods for One-Dimensional Higher Order Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2021}, volume = {14}, number = {2}, pages = {461--487}, abstract = {

Efficient and accurate Legendre spectral element methods for solving one-dimensional higher order differential equations with high oscillatory or steep gradient solutions are proposed. Some Sobolev orthogonal/biorthogonal basis functions corresponding to each subinterval are constructed, which reduce the non-zero entries of linear systems and computational cost. Numerical experiments exhibit the effectiveness and accuracy of the suggested approaches. 

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2020-0082}, url = {http://global-sci.org/intro/article_detail/nmtma/18607.html} }