On the Use of Piecewise Standard Polynomials in the Numerical Solutions of Fourth Order Boundary Value Problems

Authors

  • Md. Shafiqul Islam Department of Mathematics, University of Dhaka, Dhaka ? 1000,
  • Md. Bellal Hossain Department of Mathematics, Patuakhali Science and Technology University,

DOI:

https://doi.org/10.3329/ganit.v33i0.17659

Keywords:

Galerkin method, Fourth order linear and nonlinear BVP, Bernstein, , Bernoulli and Legendre polynomials

Abstract

This paper is devoted to find the numerical solutions of the fourth order linear and nonlinear differential equations using piecewise continuous and differentiable polynomials, such as Bernstein, Bernoulli and Legendre polynomials with specified boundary conditions. We derive rigorous matrix formulations for solving linear and non-linear fourth order BVP and special care is taken about how the polynomials satisfy the given boundary conditions. The linear combinations of each polynomial are exploited in the Galerkin weighted residual approximation. The derived formulation is illustrated through various numerical examples. Our approximate solutions are compared with the exact solutions, and also with the solutions of the existing methods. The approximate solutions converge to the exact solutions monotonically even with desired large significant digits.

GANIT J. Bangladesh Math. Soc. Vol. 33 (2013) 53-64

DOI: http://dx.doi.org/10.3329/ganit.v33i0.17659

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Published

2014-01-13

How to Cite

Islam, M. S., & Hossain, M. B. (2014). On the Use of Piecewise Standard Polynomials in the Numerical Solutions of Fourth Order Boundary Value Problems. GANIT: Journal of Bangladesh Mathematical Society, 33, 53–64. https://doi.org/10.3329/ganit.v33i0.17659

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Articles