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M. A. Ramadan, I. F. Lashien and W. K. Zahra, “Polynomial and Nonpolynomial Spline Approaches to the Numerical Solution of Second Order Boundary Value Problem,” Applied Ma-thematics and Computation, Vol. 184, No. 2, 2007, pp. 476-484. doi:10.1016/j.amc.2006.06.053.

has been cited by the following article:

• TITLE: Numerical Solutions of a Class of Second Order Boundary Value Problems on Using Bernoulli Polynomials

  AUTHORS: Md. Shafiqul Islam, Afroza Shirin

  KEYWORDS: Galerkin Method, Linear and Nonlinear BVP, Bernoulli Polynomials

  JOURNAL NAME: Applied Mathematics, Vol.2 No.9, September 19, 2011

  ABSTRACT: The aim of this paper is to find the numerical solutions of the second order linear and nonlinear differential equations with Dirichlet, Neumann and Robin 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 Dirichlet boundary conditions in the Galerkin weighted residual method. In addition to that the given differential equation over arbitrary finite domain [a,b] 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.