%0 Journal Article
%T Numerical Solutions of a Class of Second Order Boundary Value Problems on Using Bernoulli Polynomials
%A Md. Shafiqul Islam
%A Afroza Shirin
%J Applied Mathematics
%P 1059-1067
%@ 2152-7393
%D 2011
%I Scientific Research Publishing
%R 10.4236/am.2011.29147
%X The aim of this paper is to find the numerical solutions of the second order linear and nonlinear differential equations with <i>Dirichlet</i>, <i>Neumann</i> and <i>Robin</i> boundary conditions. We use the Bernoulli polynomials as linear combination to the approximate solutions of 2nd order boundary value problems. Here the Bernoulli polynomials over the interval [0,1] are chosen as trial functions so that care has been taken to satisfy the corresponding homogeneous form of the <i>Dirichlet</i> boundary conditions in the Galerkin weighted residual method. In addition to that the given differential equation over arbitrary finite domain [<i>a,b</i>] and the boundary conditions are converted into its equivalent form over the interval [0,1]. All the formulas are verified by considering numerical examples. The approximate solutions are compared with the exact solutions, and also with the solutions of the existing methods. A reliable good accuracy is obtained in all cases.
%K Galerkin Method
%K Linear and Nonlinear BVP
%K Bernoulli Polynomials
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=7168