In this study‎, ‎an efficient method is presented for solving infinite boundary integro-differential equations (IBI-DE) of the second kind with degenerate kernel in terms of Laguerre polynomials‎. ‎Properties of these polynomials and operational matrix of integration are first presented‎. ‎These properties are then used to transform the integral equation to a matrix equation which corresponds t...

Meshless methods based on the local Petrov-Galerkin approach are proposed for solution of steady and transient heat conduction problem in a continuously nonhomogeneous anisotropic medium. Fundamental solution of the governing partial differential equations and the Heaviside step function are used as the test functions in the local weak form. It is leading to derive local boundary integral equat...

In this letter we develop a new generalization of the two-dimensional differential transform method that will extend the application of the method to linear partial differential equations with spaceand time-fractional derivatives. The new generalization is based on the two-dimensional differential transform method, generalized Taylor’s formula and Caputo fractional derivative. Several illustrat...

this paper has been devoted to apply the reconstruction of variational iteration method (rvim) to handle the systems of integro-differential equations. rvim has been induced with laplace transform from the variational iteration method (vim) which was developed from the inokuti method. actually, rvim overcome to shortcoming of vim method to determine the lagrange multiplier. so that, rvim method...

Multi-walled carbon nanotubes (MWCNTs) were immobilized on the surface of a glassy carbon electrode (GCE) in the presence of cetyltrimethylammonium bromide (CTAB) to form a MWCNTs-CTAB nanocomposite-modified electrode. The electrocatalytic response of the modified electrode towards tryptophan (Trp) was investigated by cyclic voltammetry (CV) and differential pulse voltammetry (DPV). The surface...

In this paper, we report the use of crossed polarizer technique to measure differential group delay (DGD) few-mode optical fiber (FMF). The windowed Fourier transform (WFT) is applied in analysis beat length measurement spectral domain obtain dependence DGD as a function wavelength. birefringence polarization-maintaining (PMF) and FMF are measured by applying our method. We discuss noise backgr...

and Applied Analysis 3 3. Two-Dimensional Differential Transform Method The two-dimensional differential transform of function w(x, y) is defined as W(k, h) = 1 k!h! [ ∂ k+h w (x, y) ∂x∂y ] x=0 y=0 , (9) where it is noted that upper case symbol W(k, h) is used to denote the two-dimensional differential transform of a function represented by a corresponding lower case symbol w(x, y). The differe...

The solution of the complex neutron diffusion equations system in a spherical nuclear reactor is presented using homotopy perturbation method (HPM); HPM remarkable approximation that successfully solves different systems equations, and this work, solved for first time method. considered consists two consistent subsystems, where studies multi-group subsystem core, other reflector; each can deal ...