Solution of mathematical model for gas solubility using fractional-order Bhatti polynomials

Authors

Muhammad I. Bhatti, The University of Texas Rio Grande Valley
Paul Bracken, The University of Texas Rio Grande ValleyFollow
Nicholas Dimakis, The University of Texas Rio Grande ValleyFollow
Armando Herrera

Document Type

Article

Publication Date

8-13-2018

Abstract

Solutions of a mathematical model for gas solubility in a liquid are attained employing an algorithm based on the generalized Galerkin B-poly basis technique. The algorithm determines a solution of a fractional differential equation in terms of continuous finite number of generalized fractional-order Bhatti polynomial (B-poly) in a closed interval. The procedure uses Galerkin method to calculate the unknown expansion coefficients for constructing a solution to the fractional-order differential equation. Caputo?s fractional derivative is employed to evaluate the derivatives of the fractional B-polys and each term in the differential equation is converted into a matrix problem which is then inverted to construct the solution. The accuracy and efficiency of the B-poly algorithm rely on the size of the basis set as well as the degree of the B-polys used. The fractional-order B-Poly technique has been applied to the mathematical model for a gas diffusion in a liquid with gas volume functions f(t) = 1 − t1/2 and f(t) = 1 − t3/2. The solutions of the model were obtained which converged with a small number of B-polys basis set. In case of the power series solution, the solution did not converge due to alternating terms present in the solution. We used a Pade approximant on the power series solutions to extract the useful information which showed the solutions are convergent and those solutions were compared with the solutions obtained from the B-poly approach. Excellent agreement was found between the solutions. A Pade approximant was not used on the B-poly solutions because those were convergent with a smaller number of B-polys.

Comments

© 2018 The Author(s). Published by IOP Publishing Ltd

Recommended Citation

Bhatti, Muhammad, Paul Bracken, Nicholas Dimakis, and Armando Herrera. "Solution of mathematical model for gas solubility using fractional-order Bhatti polynomials." Journal of Physics Communications 2, no. 8 (2018): 085013. https://doi.org/10.1088/2399-6528/aad2fc

Creative Commons License

This work is licensed under a Creative Commons Attribution 3.0 License.

Publication Title

Journal of Physics Communications

DOI

10.1088/2399-6528/aad2fc