Article history: Received 13 October 2014 Received in revised form 17 January 2015 Accepted 18 February 2015 Available online 2 March 2015

‎in this paper, we discuss about existence of solution forintegro-differential system and then we solve it  by using the petrov-galerkin method. in the petrov-galerkin method choosing the trial and test space is important, so  we use alpert multi-wavelet as basisfunctions for these spaces. orthonormality is one of theproperties of alpert multi-wavelet which helps us to reducecomputations in the...

Article history: Received 23 April 2015 Received in revised form 3 February 2016 Accepted 31 March 2016 Available online xxxx I would like to dedicate this work to my Father, Ahmed Baccouch, who unfortunately passed away during the completion of this work

We present a study of the local discontinuous Galerkin method for transient convection-di usion problems in one dimension. We show that p degree piecewise polynomial discontinuous nite element solutions of convection-dominated problems are O( xp+2) superconvergent at Radau points. For di usion-dominated problems, the solution's derivative is O( xp+2) superconvergent at the roots of the derivati...

We construct and analyze a discontinuous Galerkin method to solve advectiondiffusion-reaction PDEs with anisotropic and semidefinite diffusion. The method is designed to automatically detect the so-called elliptic/hyperbolic interface on fitted meshes. The key idea is to use consistent weighted average and jump operators. Optimal estimates in the broken graph norm are proven. These are consiste...

In this paper we investigate the relationship between the continuous and the discontinuous Galerkin methods for elliptic problems. In particular, we show that the continuous Galerkin method can be interpreted as the limit of a discontinuous Galerkin method when a stabilization parameter tends to innnity. Based on this observation we derive a method for computing a conservative approximation of ...

An effective numerical method based on Legendre polynomials is proposed for the solution of a class of variational problems with suitable boundary conditions. The Ritz spectral method is used for finding the approximate solution of the problem. By utilizing the Ritz method, the given nonlinear variational problem reduces to the problem of solving a system of algebraic equations. The advantage o...

By the semi-inverse method, a variational principle is obtained for the Lane–Emden equation, which gives much numerical convenience when applying finite element methods or Ritz method. 2002 Elsevier Science Inc. All rights reserved.