The Numerical Approximation of the Bioheat Equation of Space-Fractional Type Using Shifted Fractional Legendre Polynomials

  • Firas A. Al-Saadawi Department Mathematics, Open Educational College in Basra, Basrah, Iraq
  • Hameeda Oda Al-Humedi Department Mathematics, College of Education for Pure Sciences, Basrah University, Basrah, Iraq
Keywords: Collocation method, Space-Fractional bioheat equation, Fractional shifted Legendre polynomials, Numerical accuracy

Abstract

The aim of this paper is to employ the fractional shifted Legendre polynomials (FSLPs) in the matrix form to approximate the fractional derivatives and find the numerical solutions of the one-dimensional space-fractional bioheat equation (SFBHE). The Caputo formula was utilized to approximate the fractional derivative. The proposed methodology applied for two examples showed its usefulness and efficiency. The numerical results showed that the utilized technique is very efficacious with high accuracy and good convergence.

Published
2020-04-26
How to Cite
Al-Saadawi, F. A., & Al-Humedi, H. O. (2020). The Numerical Approximation of the Bioheat Equation of Space-Fractional Type Using Shifted Fractional Legendre Polynomials. Iraqi Journal of Science, 61(4), 875-889. https://doi.org/10.24996/ijs.2020.61.4.21
Section
Mathematics