SCIRP Mobile Website
Paper Submission

Why Us? >>

  • - Open Access
  • - Peer-reviewed
  • - Rapid publication
  • - Lifetime hosting
  • - Free indexing service
  • - Free promotion service
  • - More citations
  • - Search engine friendly

Free SCIRP Newsletters>>

Add your e-mail address to receive free newsletters from SCIRP.

 

Contact Us >>

WhatsApp  +86 18163351462(WhatsApp)
   
Paper Publishing WeChat
Book Publishing WeChat
(or Email:book@scirp.org)

Article citations

More>>

R. L. Burden and J. D. Faires, “Numerical Analysis,” Brooks/Cole Publishing Co., Pacific Grove, 1992.

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.