A Legendre-Laguerre-Galerkin Method for Uniform Euler-Bernoulli Beam Equation

Abstract

We consider a Galerkin method based on Legendre and Laguerre polynomials and apply it to the Euler-Bernoulli beam equation. The matrices of the method are well structured, which results in substantial reduction of computational cost. Numerical examples demonstrate the efficiency and a high accuracy of the algorithm proposed.