A comparative study for fractional chemical kinetics and carbon dioxide <em>CO</em><sub>2</sub> absorbed into phenyl glycidyl ether problems

Ranbir Kumar; Sunil Kumar; Jagdev Singh; Zeyad Al-Zhour; Ranbir Kumar; Sunil Kumar; Jagdev Singh; Zeyad Al-Zhour

doi:10.3934/math.2020206

AIMS Mathematics

2020, Volume 5, Issue 4: 3201-3222. doi: 10.3934/math.2020206

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Research article

A comparative study for fractional chemical kinetics and carbon dioxide CO₂ absorbed into phenyl glycidyl ether problems

1.
Department of Mathematics, National Institute of Technology, Jamshedpur, 831014, Jharkhand, India
2.
Department of Mathematics, JECRC University, Jaipur-303905, Rajasthan, India
3.
Department of Basic Engineering Sciences, College of Engineering, Imam Abdulrahman Bin Faisal University, P. O. Box 1982, Dammam 31441, Saudi Arabia

Received: 24 October 2019 Accepted: 18 March 2020 Published: 27 March 2020
MSC : 26A33

The essential objective of this work is to implement Adam Bashforth's Moulton (ABM) and Haar wavelet method (HWM) to solve fractional chemical kinetics and another problem that relates the condensations of carbon dioxide (CO₂) and phenyl glycidyl ether (PGE) with two variety of Drichlet and a mixed set of Neumann boundary and Drichlet type conditions respectively. We have been solved the above system of differential equations by Adam Bashforth's Moulton and Haar wavelet operational method where this technique is to convert the system of differential equations into the system of algebraic equation which can be solved easily. This work is expects to contribute the vast advantage of Haar wavelets in chemical science. The Adam Bashforth's Moulton and Haar wavelet method is impressive and convenient for obtaining numerical solutions of chemical engineering type problems. A complete agreement is acheived between Adam Bashforth's Moulton solution and Haar wavelet solution. To manifest about the performance and applicability of the method, two test examples are deliberated.
- Haar wavelet method,
- Adam Bashforth’s Moulton method,
- fractional model of chemical kinetics problems,
- carbon dioxide,
- operational matrix
Citation: Ranbir Kumar, Sunil Kumar, Jagdev Singh, Zeyad Al-Zhour. A comparative study for fractional chemical kinetics and carbon dioxide CO2 absorbed into phenyl glycidyl ether problems[J]. AIMS Mathematics, 2020, 5(4): 3201-3222. doi: 10.3934/math.2020206

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Abstract

The essential objective of this work is to implement Adam Bashforth's Moulton (ABM) and Haar wavelet method (HWM) to solve fractional chemical kinetics and another problem that relates the condensations of carbon dioxide (CO₂) and phenyl glycidyl ether (PGE) with two variety of Drichlet and a mixed set of Neumann boundary and Drichlet type conditions respectively. We have been solved the above system of differential equations by Adam Bashforth's Moulton and Haar wavelet operational method where this technique is to convert the system of differential equations into the system of algebraic equation which can be solved easily. This work is expects to contribute the vast advantage of Haar wavelets in chemical science. The Adam Bashforth's Moulton and Haar wavelet method is impressive and convenient for obtaining numerical solutions of chemical engineering type problems. A complete agreement is acheived between Adam Bashforth's Moulton solution and Haar wavelet solution. To manifest about the performance and applicability of the method, two test examples are deliberated.

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