A Hermite Polynomial Approach for Solving the SIR Model of Epidemics

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Seçer A., Özdemir N., Bayram A. M.

MATHEMATICS, cilt.6, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 6
  • Basım Tarihi: 2018
  • Doi Numarası: 10.3390/math6120305
  • Dergi Adı: MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: SIR model, Hermite collocation method, approximate solution, Hermite polynomials and series, collocation points, GALERKIN METHOD, SYSTEMS
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

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.