In former articles we have given a formula for the error committed when interpolating a several times differentiable function by the sinc interpolant on a fixed finite interval. In the present workwe demonstrate the relevance of the formula through several applications: correction of the interpolant through the insertion of derivatives to increase its order of convergence, improvement of the ba...

In this paper, the numerical solution of nonlinear Fredholm integral equations of second kind is considered by Sinc method. This numerical method combines a discrete Sinc collocation method with the Newton iterative process that involves solving a nonlinear system of equations. We provide an error analysis for the method. So far approximate solutions with polynomial convergence have been report...

The sinc-collocation method is presented for solving a nonlinear system of second-order boundary value problems. Some properties of the sinc-collocation method required for our subsequent development are given and are utilized to reduce the computation of solution of the system of second-order boundary value problems to some algebraic equations. Numerical examples are included to demonstrate th...

In this paper we solve two biharmonic problems over a square, B = (−1, 1) × (−1, 1). (1) The problem ∇4U = f , for which we determine a particular solution, U , given f , via use of Sinc convolution; and (2) The boundary value problem ∇4V = 0 for which we determine V given V = g and normal derivative Vn = h on ∂B, the boundary of B. The solution to this problem is carried out based on the identity

We propose a method based on sinc series approximations for computing the Rayleigh-Sommerfeld and Fresnel diffraction integrals of optics. The are given in terms convolution, our proposed numerical approach is not only super-algebraically convergent, but it also satisfies an important property convolution—namely, preservation bandwidth. Furthermore, accuracy depends how well source field approx...

Introduction: Hadamard-encoded (H-encoded) fMRI [1] is a method that acquires a slab of multiple subslices with each RF excitation [2]. The subslices can then be extracted using temporal filtering, analogous to UNFOLD [3]. By setting the subslice width equal to that of a conventional fMRI scan, SNR is increased because of the larger slab thickness. However, since H-encoding uses complex data fo...