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Comparison of Two Numerical Schemes of the Fractional Chemical Model
  • Khaled Mohammed SAAD,
  • Khaled M Saad
Khaled Mohammed SAAD
Author Profile
Khaled M Saad
Department of Mathematics, Faculty of Applied Science, Taiz University, Department of Mathematics, College of Arts and Sciences, Kingdom of Saudi Arabia, Najran University

Abstract

This article analyzes and compares the two algorithms for the numerical solutions of the fractional isothermal chemical equations (FICEs) based on mass action kinetics for autocatalytic feedback, involving the conversion of a reactant in the Liouville-Caputo sense. The first method is based upon the spectral collocation method (SCM), where the properties of Legendre polynomials are utilized to reduce the FICEs to a set of algebraic equations. We then use the well-known method like Newton-Raphson method (NRM) to solve the set of algebraic equations. The second method is based upon the properties of Newton polynomial interpolation (NPI) and the fundamental theorem of fractional calculus. We utilize these methods to construct the numerical solutions of the FICEs. The accuracy and effectiveness of these methods is satisfied graphically by combining the numerical results and plotting the absolute error. Also, the absolute errors are tabulated, and a good agreement found in all cases. 2020 Mathematics Subject Classification: 34A08; 35A22; 41A30; 65N22.