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A numerical solution of fractional reaction-convection-diffusion for modeling PEM fuel cells based on a meshless approach. (English) Zbl 1537.65100


MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35K57 Reaction-diffusion equations
Full Text: DOI

References:

[1] Fendoğlu, H.; Bozkaya, C.; Tezer-Sezgin, M., DBEM and DRBEM solutions to 2D transient convection-diffusion-reaction type equations, Eng Anal Bound Elem, 93, 124-134 (2018) · Zbl 1403.76074
[2] Cao, Y.; Wu, Y.; Fu, L.; Jermsittiparsert, K.; Razmjooy, N., Multi-objective optimization of a PEMFC based CCHP system by meta-heuristics, Energy Rep, 5, 1551-1559 (2019)
[3] Alizadeh, M.; Torabi, F., Precise PEM fuel cell parameter extraction based on a self-consistent model and SCCSA optimization algorithm, Energy Convers Manage, 229, Article 113777 pp. (2021)
[4] Hosseini, V. R.; Zou, W., The peridynamic differential operator for solving time-fractional partial differential equations, Nonlinear Dynam, 109, 3, 1823-1850 (2022)
[5] Blanco-Cocom, L.; Botello-Rionda, S.; Ordoñez, L. C.; Valdez, S. I., A reaction-convection-diffusion model for PEM fuel cells, Finite Elem Anal Des, 201, Article 103703 pp. (2022)
[6] McLean, W.; Mustapha, K.; Ali, R.; Knio, O., Well-posedness of time-fractional advection-diffusion-reaction equations, Fract Calc Appl Anal, 22, 4, 918-944 (2019) · Zbl 1439.35542
[7] Hosseini, V. R.; Mehrizi, A. A.; Gungor, A.; Afrouzi, H. H., Application of a physics-informed neural network to solve the steady-state Bratu equation arising from solid biofuel combustion theory, Fuel, 332, Article 125908 pp. (2023)
[8] Haghighi, D.; Abbasbandy, S.; Shivanian, E.; Dong, L.; Atluri, S. N., The fragile points method (FPM) to solve two-dimensional hyperbolic telegraph equation using point stiffness matrices, Eng Anal Bound Elem, 134, 11-21 (2022) · Zbl 1521.65114
[9] Hosseini, V. R.; Shivanian, E.; Chen, W., Local radial point interpolation (MLRPI) method for solving time fractional diffusion-wave equation with damping, J Comput Phys, 312, 307-332 (2016) · Zbl 1352.65348
[10] Hidayat, M. I.P., Meshless finite difference method with B-splines for numerical solution of coupled advection-diffusion-reaction problems, Int J Therm Sci, 165, Article 106933 pp. (2021)
[11] Biglari, M.; Soheili, A. R.; Toutounian, F., A stable RBF-FD method for solving two-dimensional variable-order time fractional advection-diffusion equation, Eng Anal Bound Elem, 152, 582-597 (2023) · Zbl 1539.65133
[12] Hosseini, V. R.; Zheng, H.; Zou, W., An efficient meshfree computational approach to the analyze of thermoelastic waves of functionally graded materials in a two-dimensional space, Alexandria Eng J, 61, 12, 10495-10510 (2022)
[13] Hidayat, M. I.P.; Fajarin, R., A meshless generalized finite difference method for 2D elasticity problems, Eng Anal Bound Elem, 117, 89-103 (2020) · Zbl 1464.74364
[14] Zheng, H.; Zhou, C.; Yan, D.-J.; Wang, Y.-S.; Zhang, C., A meshless collocation method for band structure simulation of nanoscale phononic crystals based on nonlocal elasticity theory, J Comput Phys, 408, Article 109268 pp. (2020) · Zbl 07505606
[15] Hidayat, M. I.P., Meshless local B-spline collocation method for heterogeneous heat conduction problems, Eng Anal Bound Elem, 101, 76-88 (2019) · Zbl 1464.80042
[16] Zheng, H.; Zhang, C.; Yang, Z., A local radial basis function collocation method for band structure computation of 3D phononic crystals, Appl Math Model, 77, 1954-1964 (2020) · Zbl 1481.74117
[17] Hidayat, M. I.P.; Wahjoedi, B. A.; Parman, S.; Yusoff, P. S.M., Meshless local B-spline-FD method and its application for 2D heat conduction problems with spatially varying thermal conductivity, Appl Math Comput, 242, 236-254 (2014) · Zbl 1334.80012
[18] Zheng, H.; Yang, Z.; Zhang, C.; Tyrer, M., A local radial basis function collocation method for band structure computation of phononic crystals with scatterers of arbitrary geometry, Appl Math Model, 60, 447-459 (2018) · Zbl 1480.74169
[19] Jannelli, A.; Ruggieri, M.; Speciale, M. P., Analytical and numerical solutions of time and space fractional advection-diffusion-reaction equation, Commun Nonlinear Sci Numer Simul, 70, 89-101 (2019) · Zbl 1464.35396
[20] Mustapha, K., An L1 approximation for a fractional reaction-diffusion equation, a second-order error analysis over time-graded meshes, SIAM J Numer Anal, 58, 2, 1319-1338 (2020) · Zbl 1434.65129
[21] Wang, F.; Zhang, Z.; Zhou, Z., A spectral Galerkin approximation of optimal control problem governed by fractional advection-diffusion-reaction equations, J Comput Appl Math, 386, Article 113233 pp. (2021) · Zbl 1456.49026
[22] Hafez, R. M.; Zaky, M. A.; Hendy, A. S., A novel spectral Galerkin/Petrov-Galerkin algorithm for the multi-dimensional space-time fractional advection-diffusion-reaction equations with nonsmooth solutions, Math Comput Simulation, 190, 678-690 (2021) · Zbl 1540.65375
[23] Haq, S.; Hussain, M.; Ghafoor, A., A computational study of variable coefficients fractional advection-diffusion-reaction equations via implicit meshless spectral algorithm, Eng Comput, 36, 4, 1243-1263 (2020)
[24] Shivanian, E., Local radial basis function interpolation method to simulate 2D fractional-time convection-diffusion-reaction equations with error analysis, Numer Methods Partial Differential Equations, 33, 3, 974-994 (2017) · Zbl 1370.65041
[25] Shirzadi, A.; Ling, L.; Abbasbandy, S., Meshless simulations of the two-dimensional fractional-time convection-diffusion-reaction equations, Eng Anal Bound Elem, 36, 11, 1522-1527 (2012) · Zbl 1352.65263
[26] Cui, M., Compact exponential scheme for the time fractional convection-diffusion reaction equation with variable coefficients, J Comput Phys, 280, 143-163 (2015) · Zbl 1349.65281
[27] Qiao, Y.; Zhao, J.; Feng, X., A compact integrated RBF method for time fractional convection-diffusion-reaction equations, Comput Math Appl, 77, 9, 2263-2278 (2019) · Zbl 1442.65297
[28] Zhou, J. G.; Haygarth, P. M.; Withers, P. J.A.; Macleod, C. J.A.; Falloon, P. D.; Beven, K. J.; Ockenden, M. C.; Forber, K. J.; Hollaway, M. J.; Evans, R., Lattice Boltzmann method for the fractional advection-diffusion equation, Phys Rev E, 93, 4, 43310 (2016)
[29] Jian, H.-Y.; Huang, T.-Z.; Ostermann, A.; Gu, X.-M.; Zhao, Y.-L., Fast IIF-WENO method on non-uniform meshes for nonlinear space-fractional convection-diffusion-reaction equations, J Sci Comput, 89, 1, 1-29 (2021) · Zbl 1500.65042
[30] Chen, J.; Tepljakov, A.; Petlenkov, E.; Chen, Y.; Zhuang, B., Boundary Mittag-Leffler stabilization of coupled time fractional order reaction-advection-diffusion systems with non-constant coefficients, Systems Control Lett, 149, Article 104875 pp. (2021) · Zbl 1478.93499
[31] Benito, J. J.; Urena, F.; Gavete, L., Influence of several factors in the generalized finite difference method, Appl Math Model, 25, 12, 1039-1053 (2001) · Zbl 0994.65111
[32] Gavete, L.; Gavete, M. L.; Benito, J., Improvements of generalized finite difference method and comparison with other meshless method, Appl Math Model, 27, 10, 831-847 (2003) · Zbl 1046.65085
[33] Benito, J. J.; Urena, F.; Gavete, L., Solving parabolic and hyperbolic equations by the generalized finite difference method, J Comput Appl Math, 209, 2, 208-233 (2007) · Zbl 1139.35007
[34] Prelec, D., The probability weighting function, Econometrica, 497-527 (1998) · Zbl 1009.91007
[35] Benito, J. J.; Urena, F.; Gavete, L.; Alvarez, R., An h-adaptive method in the generalized finite differences, Comput Methods Appl Mech Engrg, 192, 5-6, 735-759 (2003) · Zbl 1024.65099
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