Abstract: In this article a numerical method is proposed to approximate the solution of the system of integrodifferential equations describing biological species living together. The method is based upon Legendre multiwavelet approximations. The properties of Legendre multiwavelet are first presented. These properties together with Ritz-Galerkin method are then utilized to reduce the equations ...

The so-called Ritz–Galerkin method is one of the most fundamental tools of modern computing. Its origins lie in Hilbert’s “direct” approach to the variational calculus of Euler– Lagrange and in the thesis of Walther Ritz, who died 100 years ago at the age of 31 after a long battle with tuberculosis. The thesis was submitted in 1902 in Göttingen, during a period of dramatic developments in physi...

In order to solve the boundary value problems of elliptic equations, especially with singularities and unbounded domains, the simplified hybrid-combined method, which is equivalent to the coupling method of Zienkiewicz et al. [15], is presented. This is a combination of the Ritz-Galerkin and the finite element methods. Its optimal error estimates are proved in this paper, and the solution strat...

In this paper, a continuum model based on the nonlocal elasticity theory is developed for vibration analysis of embedded orthotropic circular and elliptical micro/nano-plates. The nano-plate is bounded by a Pasternak foundation. Governing vibration equation of the nonlocal nano-plate is derived using Nonlocal Classical Plate Theory (NCPT). The weighted residual statement and the Galerkin method...

We analyze the Ritz–Galerkin method for symmetric eigenvalue problems and prove a priori eigenvalue error estimates. For a simple eigenvalue, we prove an error estimate that depends mainly on the approximability of the corresponding eigenfunction and provide explicit values for all constants. For a multiple eigenvalue we prove, in addition, apparently the first truly a priori error estimates th...

Abstract: In this paper a type of inverse problem belongs to the class of parabolic equations is considered. The approximation of the problem is based on the Ritz-Galerkin method. This approximation provides greater flexibility in which to impose initial and boundary conditions. The results of numerical experiments are compared with analytical solutions and perspicuous examples are included to ...

1 Why and how The Lanczos method is quite eeective if the desired eigenvalue is either max or min and if this eigenvalue is relatively well separated from the remaining spectrum, or when the method is applied with (A ? I) ?1 , for some reasonable guess for an eigenvalue. If none of these conditions is fulllled, for instance the computation of a vector (A ? I) ?1 y for given y may be computation...