A lower bound on the sinc function is given. Application for the sequence {b(n)}(n=1)(∞) which related to Carleman inequality is given as well.

Prolate spheroidal wave functions have recently attracted much attention in applied harmonic analysis, signal processing, and mathematical physics. They are eigenvectors of the sinc-kernel operator Qc: time- band-limiting operator. The corresponding eigenvalues play a key role, aim this paper is to obtain precise non-asymptotic estimates with explicit constants related spectrum Qc. This issue r...

The sinc method is known as an ecient numerical method for solving ordinary or par-tial dierential equations but the system of dierential equations has not been solved by this method which is the focus of this paper. We have shown that the proposed version of sinc is able to solve sti system while Runge-kutta method can not able to solve. Moreover, Due to the great attention to mathematical mod...

Nonlinear parabolic equations; Singularly perturbed equations; Sinc collocation method; Convergence analysis Abstract We propose a numerical method for solving singularly perturbed one-dimensional nonlinear parabolic problems. The equation converted to the nonlinear ordinary differential equation by discretization first in time then subsequently in each time level we use the Sinc collocation me...

1 Interpolatory basis function 2 (t) and its rst and second derivatives 0 2 (t) and 00 2 (t). 11 2 Interpolation of the function f(t) = e t sin(t); t = 0; 0:125; 0:25; :::; 10 (solid line) using the interpolatory subdivision scheme (dotted line) and the Shannon bases sinc(t) (shown using points). The interpolating points are taken at t = 0 Abstract The initialization of wavelet transforms and t...

By introducing a variable substitution we transform the two-point boundary value problem of a third-order ordinary differential equation into a system of two second-order ordinary differential equations. We discretize this order-reduced system of ordinary differential equations by both sinc-collocation and sinc-Galerkin methods, and average these two discretized linear systems to obtain the tar...

We study the Newton method and a fixed-point method for solving the system of nonlinear equations arising from the Sinc-Galerkin discretization of the Burgers equations. In each step of the Newton method or the fixedpoint method, a structured subsystem of linear equations is obtained and needs to be solved numerically. In this paper, preconditioning techniques are applied to solve such linear s...