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Open AccessArticle

A Hermite Polynomial Approach for Solving the SIR Model of Epidemics

1
Department of Mathematical Engineering, Yildiz Technical University, Istanbul 34200, Turkey
2
Department of Computer Engineering, Gelisim University, Istanbul 34315, Turkey
*
Author to whom correspondence should be addressed.
Mathematics 2018, 6(12), 305; https://doi.org/10.3390/math6120305
Received: 2 October 2018 / Revised: 27 November 2018 / Accepted: 27 November 2018 / Published: 5 December 2018
In this paper, the problem of the spread of a non-fatal disease in a population is solved by using the Hermite collocation method. Mathematical modeling of the problem corresponds to a three-dimensional system of nonlinear ODEs. The presented scheme reduces the problem to a nonlinear algebraic equation system by expanding the approximate solutions by using Hermite polynomials with unknown coefficients. These coefficients of the Hermite polynomials are computed by using the matrix operations of derivatives together with the collocation method. Maple software is used to carry out the computations. In addition, comparison of our method with the Homotopy perturbation method (HPM) and Laplece-Adomian decomposition method (LADM) proves accuracy of solution. View Full-Text
Keywords: SIR model; Hermite collocation method; approximate solution; Hermite polynomials and series; collocation points SIR model; Hermite collocation method; approximate solution; Hermite polynomials and series; collocation points
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Secer, A.; Ozdemir, N.; Bayram, M. A Hermite Polynomial Approach for Solving the SIR Model of Epidemics. Mathematics 2018, 6, 305.

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