4 citations · 7 across the 4 of their papers we have counts for
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Eigenvalue Analysis and Applications of the Legendre Dual-Petrov-Galerkin Methods for Initial Value Problems
Desong Kong, Jie Shen, Li-Lian Wang +1
In this paper, we show that the eigenvalues and eigenvectors of the spectral discretisation matrices resulted from the Legendre dual-Petrov-Galerkin (LDPG) method for the th-ord…
Fast linear barycentric rational interpolation for singular functions via scaled transformations
Desong Kong, Shuhuang Xiang
In this paper, applied strictly monotonic increasing scaled maps, a kind of well-conditioned linear barycentric rational interpolations are proposed to approximate functions of sin…
Convergence rates of spectral orthogonal projection approximation for functions of algebraic and logarithmatic regularities
Shuhuang Xiang
Based on the Hilb type formula between Jacobi polynomials and Bessel functions, optimal decay rates on Jacobi expansion coefficients are derived, by applying van der Corput type le…
Levin methods for highly oscillatory integrals with singularities
Yinkun Wang, Shuhuang Xiang
In this paper, new Levin methods are presented for calculating oscillatory integrals with algebraic and/or logarithmic singularities. To avoid singularity, the technique of singula…