A novel spectral Galerkin/Petrov–Galerkin algorithm for the multi-dimensional space–time fractional advection–diffusion–reaction equations with nonsmooth solutions
The usual classical polynomials-based spectral Galerkin and Petrov–Galerkin methods
enjoy high-order accuracy for problems with smooth solutions. However, their accuracy and …
enjoy high-order accuracy for problems with smooth solutions. However, their accuracy and …
Pointwise error estimates and local superconvergence of Jacobi expansions
As one myth of polynomial interpolation and quadrature, Trefethen [Math. Today (Southend-
on-Sea) 47 (2011), pp. 184–188] revealed that the Chebyshev interpolation of $| xa| $(with …
on-Sea) 47 (2011), pp. 184–188] revealed that the Chebyshev interpolation of $| xa| $(with …
Optimal error estimates for chebyshev approximations of functions with endpoint singularities in fractional spaces
R Xie, B Wu, W Liu - Journal of Scientific Computing, 2023 - Springer
In this paper, we introduce some new definitions and more general results of fractional
spaces in order to deal with functions with endpoint singularities. Based on this theoretical …
spaces in order to deal with functions with endpoint singularities. Based on this theoretical …
Log orthogonal functions: approximation properties and applications
We present two new classes of orthogonal functions, log orthogonal functions and
generalized log orthogonal functions, which are constructed by applying a mapping to …
generalized log orthogonal functions, which are constructed by applying a mapping to …
Asymptotic coefficients and errors for Chebyshev polynomial approximations with weak endpoint singularities: Effects of different bases
When one solves differential equations by a spectral method, it is often convenient to shift
from Chebyshev polynomials T n (x) with coefficients an to modified basis functions that …
from Chebyshev polynomials T n (x) with coefficients an to modified basis functions that …
Optimal decay rates on the asymptotics of orthogonal polynomial expansions for functions of limited regularities
S Xiang, G Liu - Numerische Mathematik, 2020 - Springer
In this paper, new and optimal asymptotics on the decay of the coefficients for functions of
limited regularity expanded in terms of Jacobi and Gegenbauer polynomial series are …
limited regularity expanded in terms of Jacobi and Gegenbauer polynomial series are …
How much faster does the best polynomial approximation converge than Legendre projection?
H Wang - Numerische Mathematik, 2021 - Springer
We compare the convergence behavior of best polynomial approximations and Legendre
and Chebyshev projections and derive optimal rates of convergence of Legendre …
and Chebyshev projections and derive optimal rates of convergence of Legendre …
Optimal convergence analysis of Laguerre spectral approximations for analytic functions
H Wang - arXiv preprint arXiv:2304.05744, 2023 - arxiv.org
In this paper, we present a comprehensive convergence analysis of Laguerre spectral
approximations for analytic functions. By exploiting contour integral techniques from …
approximations for analytic functions. By exploiting contour integral techniques from …
Convergence rates on spectral orthogonal projection approximation for functions of algebraic and logarithmatic regularities
S Xiang - SIAM Journal on Numerical Analysis, 2021 - SIAM
Based on the Hilb type formula between Jacobi polynomials and Bessel functions, optimal
decay rates on the Jacobi expansion coefficients are derived by applying van der Corput …
decay rates on the Jacobi expansion coefficients are derived by applying van der Corput …
Comparisons of best approximations with Chebyshev expansions for functions with logarithmic endpoint singularities
X Zhang - Numerical Algorithms, 2023 - Springer
The best polynomial approximation and the Chebyshev approximation are both important in
numerical analysis. In tradition, the best approximation is regarded as better than the …
numerical analysis. In tradition, the best approximation is regarded as better than the …