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https://doi.org/10.1121/1.414822

has been cited by the following article:

• TITLE: Numerical Study on Single and Multi-Dimensional Boundary Value Problems by the Method of Weighted Residual

  AUTHORS: Humaira Farzana, Md. Abdul Alim

  KEYWORDS: Eigenvalues, Heat Equation, Wave Equation, Bernstein Polynomials, Galerkin MWR

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.10 No.2, May 13, 2020

  ABSTRACT: The Galerkin method of weighted residual (MWR) for computing natural frequencies of some physical problems such as the Helmholtz equation and some second-order boundary value problems has been revised in this article. The use of one and two-dimensional characteristic Bernstein polynomials as the basis functions have been presented by the Galerkin MWR. The vibration of non-homogeneous membranes with Dirichlet type boundary conditions is also studied here. The useful properties of Bernstein polynomials, its derivatives and function approximations have also been illustrated. Besides, the efficiency and applicability of the proposed technique have been demonstrated through some numerical experiments.