in this paper, we introduce a family of fractional-order chebyshev functions based on the classical chebyshev polynomials. we calculate and derive the operational matrix of derivative of fractional order $gamma$ in the caputo sense using the fractional-order chebyshev functions. this matrix yields to low computational cost of numerical solution of fractional order differential equations to the ...

in the present article, a numerical method is proposed for the numerical solution of thekdv equation by using a new approach by combining cubic b-spline functions. in this paper we convert the kdv equation to system of two equations. the method is shown to be unconditionally stable using von-neumann technique. to test accuracy the error norms2l, ∞l are computed. three invariants of motion are p...

the aim of this paper is to present a numerical method for singularly perturbed convection-diffusion problems with a delay. the method is a combination of the asymptotic expansion technique and the reproducing kernel method (rkm). first an asymptotic expansion for the solution of the given singularly perturbed delayed boundary value problem is constructed. then the reduced regular delayed diffe...

in this study, the mechanical behavior of vanyar dam was evaluated at the end of construction. a two-dimensional numerical analysis was conducted based on a finite element method on the largest cross-section of the dam. the data recorded by the instruments located in the largest cross-section were compared with the results of the numerical analysis at the place of instruments. the settlement, p...

in this paper, using numerical methods and test results, the behavior of reinforced concrete beams strengthened with fiber-reinforced polymers (frp) is investigated. in the numerical analysis, the concrete damaged plasticity model is used for considering the nonlinear behavior and strain softening of concrete. the abaqus finite element program is utilized for the analysis of 12 flexural beams s...

the paper presents the semi-numerical solution for the magnetohydrodynamic (mhd) viscous flow due to a stretching sheet caused by boundary layer of an incompressible viscous flow. the governing partial differential equations of momentum equations are reduced into a nonlinear ordinary differential equation (node) by using a classical similarity transformation along with appropriate boundary cond...

in this work, we present a numerical method for solving nonlinear fredholmand volterra integral equations of the second kind which is based on the useof block pulse functions(bpfs) and collocation method. numerical examplesshow eciency of the method.

An unpublished example due to Joe Harris from 1983 (or earlier) gave two smooth space curves with the same Hilbert function, but one of the curves was arithmetically CohenMacaulay (ACM) and the other was not. Starting with an arbitrary homogeneous ideal in any number of variables, we give two constructions, each of which produces, using a finite number of basic double links, an ideal with the H...

1 June 1, 1998 Introduction It has long been known that modular arithmetic often produces interesting numerical patterns. These patterns can be made easier to comprehend and more interesting by rendering them as images with colors associated with numerical values. The example most often cited is Pascal’s Triangle, which exhibits the binomial coefficients. If you take the coefficients modulo m f...

Solutions to Einstein’s equations of general relativity describe, among other things, the generation and propagation of gravitational waves. Interest in numerical relativity has been bolstered by the recent construction of gravitational wave observatories such as LIGO (the Laser Interferometric Gravitational-wave Observatory). This NSF-supported project consists of two observatories (near Hanfo...