The standard multigrid procedure performs poorly or may break down when used to solve certain problems. The wavelet multigrid method solves this problem by using a wavelet transform and Schur complements to determine the coarse grid and intergrid transfer operators. This method, previously applied to diffusion and advection-dominated advection-diffusion problems, here is modified for applicatio...

in this paper, we use modified laplace decomposition method to solving initial value problems (ivp) of the second order ordinary differential equations. theproposed method can be applied to linear and nonlinearproblems

The study of the stability of differential equations without its explicit solution is of particular importance. There are different definitions concerning the stability of the differential equations system, here we will use the definition of the concept of Lyapunov. In this paper, first we investigate stability analysis of distributed order fractional differential equations by using the asympto...

When unity reflectance is approached, the Fourier-transform method of calculating the reflectance spectrum of an optical grating modulated by a slowly varying envelope becomes unacceptably inaccurate. The modified Fourier transform method of Bovard [Appl. Opt. 29, 24 (1990)] can achieve complete accuracy for quarter-wave gratings. We report herein the extension of Bovard's method to non-quarter...

In this article we have considered a non-standard finite difference method for the solution of second order  Fredholm integro differential equation type initial value problems. The non-standard finite difference method and the composite trapezoidal quadrature method is used to transform the Fredholm integro-differential equation into a system of equations. We have also developed a numerical met...

Abstract In this work, a technique for finding approximate solutions ordinary fraction differential equations (OFDEs) of any order has been proposed. The method is hybrid between Galerkin and collocation methods. Also, can be extended to fractional integro-differential (FIDEs) optimal control problems (FOCPs). spatial approximations with their derivatives are based on shifted ultraspherical pol...

This paper presents a new method for exponential Radon transform inversion based on the harmonic analysis of the Euclidean motion group of the plane. The proposed inversion method is based on the observation that the exponential Radon transform can be modified to obtain a new transform, defined as the modified exponential Radon transform, that can be expressed as a convolution on the Euclidean ...

In this paper, the effect of elastic foundation on the out of plane displacement of functionally graded circular plates using differential transform method is presented. Differential transform method is a semi-analytical-numerical solution technique that is capable to solve various types of differential equations. Using this method, governing differential equations are transformed into recursiv...