We design a wavelet optimized finite difference (WOFD) scheme for solving self-adjoint singularly perturbed boundary value problems. The method is based on an interpolating wavelet transform using polynomial interpolation on dyadic grids. Small dissipation of the solution is captured significantly using an adaptive grid. The adaptive feature is performed automatically by thresholding the wavele...

Second and fourth order convergent methods based on Quartic nonpolynomial spline function are presented for the numerical solution of a third order two-point boundary value problem. The proposed approach gives better approximations than existing polynomial spline and finite difference methods and has a lower computational cost. Convergence analysis of the proposed method is discussed; two numer...

The degree of automation at U.S. manufacturing plants differs widely across metropolitan areas. This paper examines the effect skill mix in a metropolitan area has on the degree of automation at plants in the area. In markets with a higher relative availability of lessskilled labor, comparable plants – even plants in the same narrow (4-digit SIC) industries – use less automation. The results ho...

Laser direct-write patterning methods are traditionally limited by the diffraction limit to size scales several hundreds of nanometers at the minimum. In this work, we demonstrate a new method of laser based patterning that overcomes these limitations by taking advantage of near-field enhancement at the surface of dielectric microspheres. Polystyrene microspheres are trapped in CW Bessel beam l...

An important property for finite difference schemes designed on curvilinear meshes is the exact preservation of free-stream solutions. This property is difficult to fulfill for high order conservative essentially non-oscillatory (WENO) finite difference schemes. In this paper we explore an alternative flux formulation for such finite difference schemes [5] which can preserve free-stream solutio...

Quartic non-polynomial splines are used to develop a new numerical method for computing approximations to the solution of a system of third-order boundary-value problems associated with obstacle, unilateral, and contact problems. It is shown that the new method gives approximations, which are better than those produced by other collocation, finite-difference, and spline methods. Convergence ana...

© journal de afrikana www.jdeafrikana.com 233 Original Research Article ISSN; 2411-1376 Title: Uniformly Convergent Second Order Completely Fitted Finite Difference Scheme for Two-Parameters Singularly Perturbed Two Point Boundary Value Problem K. Phaneendra*, G. Mahesh Department of Mathematics, University College of Science, Saifabad, Osmania University, Hyderabad, India _____________________...

In this article we consider a non-standard finite difference method for numerical solution of linear Fredholm integro-differential equations. The non-standard finite difference method and the repeated / composite trapezoidal quadrature method are used to transform the Fredholm integrodifferential equation into a system of non-linear algebraic equations. The numerical experiments on some linear ...