PERFORMANCE COMPARISON OF SPREAD AND BERNSTEIN BASIS IN THE SOLUTION OF FRACTIONAL DIFFERENTIAL EQUATION VIA COLLOCATION METHOD

Authors

  • A. S. Olagunju Department of Mathematics, Federal University of Lafia, Nigeria. Author
  • F. L Joseph Department of Mathematical Sciences, Bingham University Karu, Nigeria. Author
  • Y. E. Atanyi Department of Mathematics, Federal University of Lafia, Nigeria. Author

Keywords:

Bernstein polynomial, Spread polynomial, Caputo Fractional Derivative, Fractional differential equations

Abstract

In this article, basis functions of Spread and Bernstein polynomials are linearly combined with unknown coefficients. These linear combinations are applied in formulating approximate solution for fractional differential equations. Residual equation derived from the fractional differential equation is collocated at equally spaced interval of the boundary where the problem exists. Systems of equation
derived from this approach is solved and values of coefficients are obtained. Numerical solution of the problem is arrived at by substituting values of the coefficients into constructed linear combinations. To illustrate the effectiveness of these two polynomials, comparison between the two over a varying degree n of the approximants is carried out. This is done alongside the analytical solution of each problem. The discrepancies obtained speak in favour of the proposed methods. Mathematics subject classification: 65L10, 65L60

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References

I. Podlubny, fractional Differential Equations, Academic Press, San Diego, 1999

S. B. Yuste and L. Acedo, “ An explicit Finite Difference Method and a new Von Newmann-type Stability Analysis for Fractional diffusion equations”, SIAM Journal on Numerical Analysis, vol. 42, 5, pp. 1862 – 1874, 2005.

X-J Yang, J. A. Tenreiro Machado, D Baleanu; On exact traveling-wave solutions for local fractional Korteweg-de vries equation. Chaos 2016; 26:084312.

X-J Yang, F. Gao and H. M. Srivastava; Exact travelling wave solutions for the local fractional two-dimensional Burgers-type equations. Comput Math Appl 2017; 73: 203-210

Y. Zhang, D. Baleanu and X-J Yang. New solutions of the transport equations in porous media within local fractional derivatives. Proc Rom Acad 2016; 17: 230 - 236

C. Li; and S. Sarwar; Existence and Continuation of Solution for Caputo type fractional differential equations. Electron. J. Differ. Eqution, pp 1 – 14, 2016.

R, Gorenflo; A. A. Kilbas; F. Mainardi; S. V. Rogosin; Mittage-Leffer Function, Related topics and application; Springer: New York, NY, USA, 2014

B. Ross, Fractional calculus: an historical apologia for the development of a calculus using differentiation and anti differentiation of non integer orders, Mathematics Magazine, vol. 50, no. 3, May 1977, pp. 115-122.

Fakhrodin Mohammadi, Numerical solution of Bagley-Torvik equation using Chebyshev wavelet operational matrix of fractional derivative. International Journal of Applied Mathematics and Machanics, 2(1), 2014 pp. 83 – 91.

X. Huang and X. Lu, The Use of Fractional B-Spline Wavelets in Multiterms Fractional Ordinary Differential Equations. International Journal of Differential equations. 2010. Vol. 2010, 968186.

S. Goh, Chebyshev polynomials and spread polynomials, Mathematica Scandinavia, UNSW, 2005 12]

S. Goh and N. J. Wildberger; Spread polynomials, rotations and the butterfly effect, arXiv: 0911.1025v1 [math.CA] 5 Nov

A. S. Olagunju, Numerical Solution of Nonlinear Singular Ordinary Differential Equations Arising in Biology via

Operational Matrix of Bernstein Polynomials. Journal of Nigerian Association of Mathematical Physics, 2017, vol. 43, pp 61–

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Published

2022-12-01

How to Cite

PERFORMANCE COMPARISON OF SPREAD AND BERNSTEIN BASIS IN THE SOLUTION OF FRACTIONAL DIFFERENTIAL EQUATION VIA COLLOCATION METHOD. (2022). The Transactions of the Nigerian Association of Mathematical Physics, 18, 125-132. https://nampjournals.org.ng/index.php/tnamp/article/view/163

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