A Gaussian-Sinc basis set methodology is presented for the calculation of the electronic structure of atoms and molecules at the Hartree-Fock level of theory. This methodology has several advantages over previous methods. The all-electron electronic structure in a Gaussian-Sinc mixed basis spans both the "localized" and "delocalized" regions. A basis set for each region is combined to make a ne...

planar d-bar integral equation is one of the inverse scattering solution methods for complex problems including inverse conductivity considered in applications such as electrical impedance tomography (eit). recently two different methodologies are considered for the numerical solution of d-bar integrals equation, namely product integrals and multigrid. the first one involves high computational ...

The Sinc-Galerkin method is presented as a new and potentially useful extension of the spectral method in numerical oceanography. To describe and illustrate the technique , a Sinc-Galerkin procedure is used to infer the sensitivity of wind-driven subsur-face currents in coastal regions and semi-enclosed seas when the vertical eddy viscosity coeecient is represented as a continuously diierentiab...

This paper presents meshfree method for solving systems of linear Volterra integro-differential equations with initial conditions. This approach is based on collocation method using Sinc basis functions. It's well-known that the Sinc approximate solution converges exponentially to the exact solution. Some numerical results are included to show the validity of this method.

A collocation procedure is developed for the initial value problem u′(t) = f(t, u(t)), u(0) = 0, using the globally defined sinc basis functions. It is shown that this sinc procedure converges to the solution at an exponential rate, i.e., O(M2 exp(−κ √ M)) where κ > 0 and 2M basis functions are used in the expansion. Problems on the domains R = (−∞,∞) and R+ = (0,∞) are used to illustrate the i...

A collocation procedure is developed for the linear and nonlinear Volterra integral equations, using the globally defined Sinc and auxiliary basis functions. We analytically show the exponential convergence of the Sinc collocation method for approximate solution of Volterra integral equations. Numerical examples are included to confirm applicability and justify rapid convergence of our method.

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...

in this paper, an effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (rbfs). we present an algorithm based on interpolation by radial basis functions including multiquadratics (mqs), using legendre-gauss-lobatto nodes and weights. also a theorem is proved for convergence of the algorithm. some numerical examples are presented...

Fueled by many applications in random processes, imaging science, geophysics, etc., fractional Laplacians have recently received significant attention. The key driving force behind the success of t...

In this paper, An effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (RBFs). We present an algorithm based on interpolation by radial basis functions including multiquadratics (MQs), using Legendre-Gauss-Lobatto nodes and weights. Also a theorem is proved for convergence of the algorithm. Some numerical examples are presented...