作为项目负责人获得国家自然科学青年基金和数学天元基金资助，作为主要成员参研国家自然科学基金面上项目多项。在国内外学术刊物上发表论文数篇。
Li Shan, Sun Guilei,Guo Yuling and Wang Zhongqing, A Multiple Interval Chebyshev-Gauss-Lobatto Collocation Method for Multi-Order Fractional Differential EquationsGlobal, E. Asian J. Appl. Math., 2022,12 (3), 649-672 Li Shan, Wu Jinju and Wang Zhongqing, Sobolev orthogonal Legendre rational spectral methods for exterior problems, Int. J. Comput. Math.,2022, 99 (2), 370-390 Li Shan, Lai Zhenyan, Jin Lusha and Yu Xuhong, Diagonalized Gegenbauer rational spectral methods for second- and fourth-order problems on the whole line, Appl. Numer. Math., 2020, 151, 494-516. Li Shan, Yan Shimi and Wang Zhongqing, Efficient Legendre dual-Petrov-Galerkin methods for solving odd-order differential equations , Discrete Cont Dyn-B.,2020, 25 (4), 1543-1563 Li Shan, Li Qiaoling and Wang Zhongqing, Sobolev orthogonal Legendre rational spectral methods for problems on the half line, Math. Methods Appl. Sci., 2020, 43 (1), 255-268 Qin Yonghui, Li Shan, Li Jingliang and Li Qiaoling, Multidomain Legendre-Galerkin Chebyshev collocation least squares method for one-dimensional problems with two nonhomogeneous jump conditions, Int. J. Comput. Math.,, 2019, 96 (12), 2411-2422. Li Shan, Boyd, John P., Spectral methods in non-tensor geometry, Part II: Chebyshev versus Zernike polynomials, gridding strategies and spectral extension on squircle-bounded and perturbed-quadrifolium domains, Appl. Math. Comput., 2015,269, 759-774. Li Shan, Boyd, John P., Approximation on non-tensor domains including squircles, Part III: Polynomial hyperinterpolation and radial basis function interpolation on Chebyshev-like grids and truncated uniform grids, J. Comput. Phys., 2014, 285, 653-668. Li Shan, Boyd, John P., Symmetrizing grids, radial basis functions, and Chebyshev and Zernike polynomials for the D-4 symmetry group; Interpolation within a squircle, Part I, J. Comput. Phys., 2014, 258, 931-947.
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