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

## 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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*The Transactions of the Nigerian Association of Mathematical Physics*,

*18*, 125-132. https://nampjournals.org.ng/index.php/tnamp/article/view/163