TY - JOUR T1 - Efficient and Accurate Legendre Spectral Element Methods for One-Dimensional Higher Order Problems AU - Zhang , Yang AU - Yu , Xuhong AU - Wang , Zhongqing JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 461 EP - 487 PY - 2021 DA - 2021/01 SN - 14 DO - http://doi.org/10.4208/nmtma.OA-2020-0082 UR - https://global-sci.org/intro/article_detail/nmtma/18607.html KW - Legendre spectral element methods, higher order differential equations, Sobolev orthogonal/biorthogonal basis functions, high oscillatory or steep gradient solutions. AB -

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.