Approximation Theory and Approximation Practice (“ATAP”), originally published in 2013,
concerns approximation of nonperiodic functions on the interval [− 1, 1], the Chebyshev …

An efficient algorithm for the accurate computation of Gauss--Legendre and Gauss--Jacobi
quadrature nodes and weights is presented. The algorithm is based on Newton's root …

Gauss--Legendre quadrature rules are of considerable theoretical and practical interest
because of their role in numerical integration and interpolation. In this paper, a series …

We present a brief survey on the modern tensor numerical methods for multidimensional
stationary and time-dependent partial differential equations (PDEs). The guiding principle of …

Barycentric interpolation is arguably the method of choice for numerical polynomial
interpolation. The polynomial interpolant is expressed in terms of function values using the …

We introduce an efficient numerical method for second-order linear ODEs whose solution
may vary between highly oscillatory and slowly changing over the solution interval. In …

The main purpose of this paper is to compute the weights of Clenshaw–Curtis and Fejér type
quadrature rules via DCT and DST, for general weight functions w. The approach is different …

In the high-temperature environment, a larger thermal expansion mismatch of a bimaterial
leads to pronounced thermal stresses and interface crack growth. In this paper, a …

The convergence rates on polynomial interpolation in most cases are estimated by
Lebesgue constants. These estimates may be overestimated for some special points of sets …

In this paper, we present a new pseudo-spectral method to solve the initial value problem
associated to a non-local KdV–Burgers equation involving a Caputo-type fractional …