Sinc-Collocation Method with Orthogonalization for Singular Poisson-Like Problems

Abstract

Abstract.This paper uses the Sine-collocation method to solve singular Poisson-like problems (a first-or higher-order partial derivative of the exact solution is unbounded on the boundary). A linear system is obtained which is the same as that obtained by using the Sinc-Galerkin method. With a smart choice of the stepsize and the number of the gridpoints, the orthogonalization technique is successfully applied to solve the linear system obtained, and a numerical approximation is obtained with an exponential accuracy 0(exp(-c/Vi)), where N is a truncation parameter and c is a constant independent of N .

Shock wave simulations using Sinc Differential Quadrature Method

“…The mathematical aspects of sinc interpolation were explained in Bellomo et al (2001). Sinc functions have been used as basis for many numerical methods such as Galerkin methods by El-Gamel et al (2003), Dockery (1993), El-Gamel andZayed (2002), Lund and Bowers (1992), Ralph and Bowers (1991), Stenger (1993) and Smith et al (1991) and collocation methods by Yin (1994), Bialecki (1991), Carlson et al (1997), Lund and Rilay (1984) and Bonzani (1997) to get numerical solutions of some partial differential equations. Differential quadrature method is an efficient approximation to the derivative of a function at a discrete point using linear sum of a functional values at discrete points in the whole domain.…”

Vibration Analysis of Piezoelectric Composite Plate Resting on Nonlinear Elastic Foundations Using Sinc and Discrete Singular Convolution Differential Quadrature Techniques

“…A cardinal sine function is used as a shape function, such that the unknown ψ and its derivatives can be approximated as a weighted linear sum of nodal values, ψ i , (i � −N, N), as follows [27][28][29][30][31][32]:…”

“…Additionally, there is no research in piezoelectric composite plate resting on nonlinear elastic foundations, whether analytically or numerically. e sinc differential quadrature method (SDQM) [27][28][29][30][31][32] and the discrete singular convolution differential quadrature method (DSCDQM) [33][34][35][36][37][38][39][40][41][42] are more reliable than the polynomial-based DQM.…”