The Reaction–Diffusion Models in Biomedicine: Highly Accurate Calculations via a Hybrid Matrix Collocation Algorithm
Abstract
:1. Introduction
2. A Review of a New Class of Polynomials
2.1. The Chatterjea Polynomials
2.2. Convergent of ChPs in the Sense of
3. Description of QLM–ChPs Matrix Approach
3.1. The Essence of QLM
3.2. The Main Algorithm
3.3. Theoretical Upper Bound for QLM–ChPs Approach
3.4. Error Measurement via REF Method
3.5. The RC Methodology
4. Numerical Calculations
4.1. Case Study I: Planar Particle ()
4.2. Case Study II: Spherical Particle ()
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Parameter | Description | Unit |
---|---|---|
Substrate concentration | mol/cm3 | |
Dimensionless substrate concentration () | - | |
Bulk-substrate concentration | mol/cm3 | |
Effective diffusivity inside the particle | cm3/s | |
Maximum reaction rate | mol/s cm3 | |
Michaelis constant | mol/cm3 | |
External mass-transfer coefficient | mol/cm3 | |
Spatial variable | cm | |
Thiele modulus | - | |
Dimensionless Michaelis constant | - | |
Half length of the particle | cm | |
Modified Sherwood number | - |
x | ||||
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x | ||||||
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2 | − | − | − | − | ||||
4 | ||||||||
8 | ||||||||
16 |
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Izadi, M.; Srivastava, H.M. The Reaction–Diffusion Models in Biomedicine: Highly Accurate Calculations via a Hybrid Matrix Collocation Algorithm. Appl. Sci. 2023, 13, 11672. https://doi.org/10.3390/app132111672
Izadi M, Srivastava HM. The Reaction–Diffusion Models in Biomedicine: Highly Accurate Calculations via a Hybrid Matrix Collocation Algorithm. Applied Sciences. 2023; 13(21):11672. https://doi.org/10.3390/app132111672
Chicago/Turabian StyleIzadi, Mohammad, and Hari M. Srivastava. 2023. "The Reaction–Diffusion Models in Biomedicine: Highly Accurate Calculations via a Hybrid Matrix Collocation Algorithm" Applied Sciences 13, no. 21: 11672. https://doi.org/10.3390/app132111672