There are few techniques available to numerically solve sixth-order boundary-value problems with two-point boundary conditions. In this paper we show that the Sinc-Galerkin method is a very effective tool in numerically solving such problems. The method is then tested on examples with homogeneous and nonhomogeneous boundary conditions and a comparison with the modified decomposition method is m...

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...

In this paper, a numerical procedure for solving a class of nonlinear VolterraFredholm integral equations is presented. The method is based upon the globally defined sinc basis functions. Properties of the sinc procedure are utilized to reduce the computation of the nonlinear integral equations to some algebraic equations. Illustrative examples are included to demonstrate the validity and appli...

A new algorithm is presented for solving Troesch’s problem. The numerical scheme based on the sinc-collocation technique is deduced. The equation is reduced to systems of nonlinear algebraic equations. Some numerical experiments are made. Compared with the modified homotopy perturbation technique (MHP), the variational iteration method and the Adomian decomposition method. It is shown that the ...

in this paper, the sinc collocation method is proposed for solving linear and nonlinear multi-order fractional differential equations based on the new definition of fractional derivative which is recently presented by khalil, r., al horani, m., yousef, a. and sababeh, m. in a new definition of fractional derivative, j. comput. appl. math. 264 (2014), 65{70. the properties of sinc functions are ...

Sinc-Galerkin method based upon double exponential transformation for solving Troesch's problem was given in this study. Properties of the Sinc-Galerkin approach were utilized to reduce the solution of nonlinear two-point boundary value problem to same nonlinear algebraic equations, also, the matrix form of the nonlinear algebraic equations was obtained.The error bound of the method was found. ...

The Source Galerkin method finds approximate solutions to the functional differential equations of field theories in the presence of external sources. While developing this process, it was recognized that approximations of the spectral representations of the Green’s functions by Sinc function expansions are an extremely powerful calculative tool. Specifically, this understanding makes it not on...

Up to now, no consensus exists about the electronic nature of phosphorus (P) as donor for SiO2-embedded silicon nanocrystals (SiNCs). Here, we report on hybrid density functional theory (h-DFT) calculations of P in the SiNC/SiO2 system matching our experimental findings. Relevant P configurations within SiNCs, at SiNC surfaces, within the sub-oxide interface shell and in the SiO2 matrix were ev...

A critical procedure in Synthetic Aperture Radar (SAR) Interferometric (InSAR) processing was studied: SAR image coregistration. Two pairs of ERS-1/2 SAR tandem data, representing diverse terrain types and different baselines, were used in this research. The commonly used traditional SAR image coregistration algorithms were addressed and tested; the computationally intensive algorithms were exa...