A different approach for the fractional chemical model

Authors

  • Khaled Saad Department of Mathematics, Faculty of Arts and Sciences, Najran University, Saudi ArabiaDepartment of Mathematics, Faculty of Applied Science, Taiz University, Taiz, Yemen

DOI:

https://doi.org/10.31349/RevMexFis.68.011404

Keywords:

Liouville-Caputo operator; fractional isothermal chemical; Legendre polynomials ; spectral collocation method; Newton polynomial interpolation; Newton-Raphson method

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.

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Published

2022-01-01

Issue

Section

14 Other areas in Physics