Islam, M.S. and Shirin, A. (2011) Numerical Solutions of a Class of Second Order Boundary Value Problems on Using Bernoulli Polynomials. Applied Mathematics, 2, 1059-1067.
https://doi.org/10.4236/am.2011.29147

has been cited by the following article:

• TITLE: Galerkin-Bernstein Approximations for the System of Third-Order Nonlinear Boundary Value Problems

  AUTHORS: Snigdha Dhar, Md. Shafiqul Islam

  KEYWORDS: System of Third-Order BVP, Galerkin Method, Bernstein Polynomials, Nonlinear BVP, Higher-Order BVP

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.12 No.6, June 19, 2024

  ABSTRACT: This paper is devoted to find the numerical solutions of one dimensional general nonlinear system of third-order boundary value problems (BVPs) for the pair of functions using Galerkin weighted residual method. We derive mathematical formulations in matrix form, in detail, by exploiting Bernstein polynomials as basis functions. A reasonable accuracy is found when the proposed method is used on few examples. At the end of the study, a comparison is made between the approximate and exact solutions, and also with the solutions of the existing methods. Our results converge monotonically to the exact solutions. In addition, we show that the derived formulations may be applicable by reducing higher order complicated BVP into a lower order system of BVPs, and the performance of the numerical solutions is satisfactory.