期刊论文

Wang, Li-Lian

英文

Journal of Scientific Computing

0885-7474

2017

70

2

451-477

10.1007/s10915-016-0253-2

Zhimin Zhang: The research of this author is supported in part by the National Natural Science Foundation of China (11471031 and 91430216), and the U.S. National Science Foundation (DMS-1419040). The first author would like to thank the supports from both Beijing Computational Sciences and Research Center, Beijing, China and Division of Mathematical Sciences of Nanyang Technological University, Singapore. Huiyuan Li: The research of this author is partially supported by the National Natural Science Foundation of China (91130014, 11471312 and 91430216). Jing Zhang: The work of this author is partially supported by the National Natural Science Foundation of China (11201166), and the Fundamental Research Funds for the Central Universities (CCNU15A02033).

本校为第一机构

We introduce a family of generalized prolate spheroidal wave functions (PSWFs) of order $$-1,$$ and develop new spectral schemes for second-order boundary value problems. Our technique differs from the differentiation approach based on PSWFs of order zero in Kong and Rokhlin (Appl Comput Harmon Anal 33(2):226–260,2012); in particular, our orthogonal basis can naturally include homogeneous boundary conditions without the re-orthogonalization of Kong and Rokhlin (2012). More notably, it leads to diagonal systems or direct “explic...