This talk consists of a proof of part of Stenger’s SINC-PACK computer package (an approx. 400-page tutorial + about 250 Matlab programs) that one can always achieve separation of variables when solving linear elliptic, parabolic, and hyperbolic PDE (partial differential equations) via use of Sinc methods. Some examples illustrating computer solutions via SINC-PACK will nevertheless be given in ...

This paper presents the application of Sinc method to solve second order two-point boundary value problems based on derivative interpolation. Even in the presence of singularities, the Sinc numerical method is known to exhibit exponential convergence, resulting in highly accurate solutions. However, the customary approach of interpolating the solution variable with the Sinc bases requires first...

In this paper, Solvability nonlinear Volterra integral equations with general vanishing delays is stated. So far sinc methods for approximating the solutions of Volterra integral equations have received considerable attention mainly due to their high accuracy. These approximations converge rapidly to the exact solutions as number sinc points increases. Here the numerical solution of nonlinear d...

A Sinc-collocation method has been proposed by Stenger, and he also gave theoretical analysis of the method in the case of a ‘scalar’ equation. This paper extends the theoretical results to the case of a ‘system’ of equations. Furthermore, this paper proposes more efficient method by replacing the variable transformation employed in Stenger’s method. The efficiency is confirmed by both of theor...

‎In this paper‎, ‎the numerical solutions of linear and nonlinear Volterra integral‎ ‎equations with nonvanishing delay are considered by two methods‎. ‎The methods are developed by means of‎ ‎the sinc approximation with the single exponential (SE) and double exponential (DE)‎ ‎transformations‎. ‎The existence and uniqueness of sinc-collocation solutions for these equations are provided‎. ‎Thes...

Many numerical methods have been developed for the solution of Poisson and Laplace equations such as finite-difference methods, finite-element methods, boundary-element methods, etc. Sinc numerical methods developed recently by Stenger and co-workers excel over other methods for problems involving singularities, infinite or semi-infinite domains as well as boundary layer behaviors. In this pape...

Chebfun is an established software system for computing with functions of a real variable, but its capabilities for handling functions with singularities are limited. Here an analogous system is described based on sinc function expansions instead of Chebyshev series. This experiment sheds light on the strengths and weaknesses of sinc function techniques. It also serves as a review of some of th...

Six forest tree height inversion methods of polarimetric SAR interferometry were validated using repeat pass E-SAR datasets and the corresponding ground measured forest stand height. We show that SINC, three stage full model and three stage SINC inversions have good performance, and the SINC inversion with the first optimum coherence (OPT1) produces the best result among the eleven coherence ty...