دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات45
تعداد شماره‌ها1,516
تعداد مقالات18,527
تعداد مشاهده مقاله60,634,838
تعداد دریافت فایل اصل مقاله21,546,231
Lotfi, Mahmoud. (1403). Numerical solution of different population balance models using operational method based on Genocchi polynomials. سامانه مدیریت نشریات علمی, 13(2), 659-675. doi: 10.22034/cmde.2024.60533.2591
Mahmoud Lotfi. "Numerical solution of different population balance models using operational method based on Genocchi polynomials". سامانه مدیریت نشریات علمی, 13, 2, 1403, 659-675. doi: 10.22034/cmde.2024.60533.2591
Lotfi, Mahmoud. (1403). 'Numerical solution of different population balance models using operational method based on Genocchi polynomials', سامانه مدیریت نشریات علمی, 13(2), pp. 659-675. doi: 10.22034/cmde.2024.60533.2591
Lotfi, Mahmoud. Numerical solution of different population balance models using operational method based on Genocchi polynomials. سامانه مدیریت نشریات علمی, 1403; 13(2): 659-675. doi: 10.22034/cmde.2024.60533.2591

Numerical solution of different population balance models using operational method based on Genocchi polynomials

Computational Methods for Differential Equations
مقاله 22، دوره 13، شماره 2، خرداد 2025، صفحه 659-675    اصل مقاله (448.02 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.60533.2591
نویسنده
Mahmoud Lotfi*
Department of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, Iran.
چکیده
Genocchi polynomials have exciting properties in the approximation of functions. Their derivative and integral calculations are simpler than other polynomials and, in practice, they give better results with low degrees. For these reasons, in this article, after introducing the important properties of these polynomials, we use them to approximate the solution of different population balance models. In each case, we first discuss the solution method and then do the error analysis. Since we do not have an exact solution, we compare our numerical results with those of other methods. The comparison of the obtained results shows the efficiency of our method. The validity of the presented results is indicated using MATLAB-Simulink.
کلیدواژه‌ها
Genocchi polynomials؛ Genocchi numbers؛ Population balance models؛ Error analysis؛ Numerical results
مراجع
  • [1] A. Alipanah and M. Dehghan, Solution of population balance equations via rationalized Haar functions, Kybernetes, 37 (2008), 1189–1196.
  • [2] A. Alipanah and M. Zafari, Collocation method using auto-correlation functions of compact supported wavelets for solving Volterra’s population model, Chaos, Solitons and Fractals, 175 (2023).
  • [3] I. A. Bhat, L. N. Mishra, N. N., Mishra, C. Tun, and O. Tun, Precision and efficiency of an interpolation approach to weakly singular integral equations, International Journal of Numerical Methods for Heat and Fluid Flow, 34 (2024), 1479–1499.
  • [4] J. Biazar and K. Hosseini, Analytic approximation of Volterras population model, JAMSI, 13 (2017), 5–17.
  • [5] R. Y. Chang and M. L. Wang, Shifted Legendre function approximation of differential equations; application to crystalization processes, J. Chem. Engng, 8 (1984), 117–25.
  • [6] M. Q. Chen, C. Hwang, and Y. P. Shih, A Wavelet-Galerkin method for solving population balance equations, Computers Chem. Engng, 20 (1996), 131–145.
  • [7] H. Dehestani, Y. Ordokhani, and M. Razzaghi, On the applicability of Genocchi wavelet method for different kinds of fractional order differential equations with delay, Numer, Linear Algebr., 26 (2019).
  • [8] H. Dehestani, Y. Ordokhani, and M. Razzaghi, A numerical technique for solving various kinds of fractional partial differential equations via Genocchi hybrid functions, Revista de la Real Academia de Ciencias Exactas, Fsicas y Naturales. Serie A. Matematicas, 113 (2019), 3297–3321.
  • [9] A. S. Firdous, M. Irfan, and S. N. Kottakkaran, Gegenbauer wavelet quasi-linearization method for solving fractional population growth model in a closed system, Mathematical Methods in the Applied Sciences, 45 (2022), 3605–3623.
  • [10] B. Fornberg, A practical guide to pseudospectral methods, Cambridge, 1999.
  • [11] F. Ghomanjani, A numerical method for solving Bratus problem, Palestine Journal of Mathematics, 11 (2022), 372–377.
  • [12] S. Hu, M. S. Kim, P. Moree, and M. Sha, Irregular primes with respect to Genocchi numbers and Artin’s primitive root conjecture, Journal of Number Theory 205 (2019), 50–80.
  • [13] C. Hwang and Y. P. Shih, Solutions of population balance equations via block pulse functions, J. Chem. Engng, 25 (1982), 39–45.
  • [14] A. Isah and C. Phang, Genocchi wavelet-like operational matrix and its application for solving nonlinear fractional differential equations, Open Phys., 14 (2016), 46–472.
  • [15] A. Kanwal, C. Phang, and U. Iqbal, Numerical solution of fractional diffusion wave equation and fractional KleinGordon equation via two-dimensional Genocchi polynomials with a RitzGalerkin method, Computation, 6 (2018).
  • [16] J. R. Loh. and C. Phang, A new numerical scheme for solving system of Volterra integro-differential equation, Alex. Eng. J., 57 (2018), 1117–1124.
  • [17] M. Lotfi and A. Alipnah, Implementation of auto-correlation functions of compactly supported wavelets to population balance differential equation, The 6th Seminar on Numerical Analysis and Its Applications, Maraghe, Iran (2016).
  • [18] M. M. Matar, Existence of solution involving Genocchi numbers for nonlocal anti-periodic boundary value problem of arbitrary fractional order, Revista de la Real Academia de Ciencias Exactas, Fsicas y Naturales. Serie A. Matematicas, 112 (2018), 945–956.
  • [19] S. T. Mohyud-Din, A. Yldrm, and Y. Glkanat, Analytical solution of Volterra’s population model, Journal of King Saud University - Science, 22, (2010), 247–250.
  • [20] A. D. Randolph, Effect of crystal breakage on crystal size distribution in a mixed suspension crystallizer. I and EC Fund. 8 (1969), 58–63.
  • [21] A. D. Randolph and M. A. Larson, Theory of Particulate Processes, 2nd Edn. Academic Press, New York, 1988.
  • [22] F. Rigi and H. Tajadodi, Numerical approach of fractional Abel differential equation by genocchi polynomials, International Journal of Applied and Computational Mathematics, 5 (2019), 1–11.
  • [23] S. H. Rim, K. H. Park, and E. J. Moon, On Genocchi numbers and polynomials, Abstr. Appl. Anal. 2008.
  • [24] A. Saadatmandi, A. Khani, and M. A. Azizi, A sinc-Gauss-Jacobi collocation method for solving Volterra’s population growth model with fractional order, Tbilisi Mathematical Journal 11 (2018), 123–137.
  • [25] F. M. Scudo, Vito Volterra and theoretical ecology, Teoretical Population Biology, 2 (1971), 1–23.
  • [26] P. N. Singh and D. Ramkrishna, Solution of population balance equations by WRM, Comput. Chem. Engng, 1 (1977), 23–31.
  • [27] R. D. Small, Population growth in a closed system, SIAM Review, 25 (1983), 93–95.
  • [28] H. M. Srivastava, F. A. Shah, and M. Irfan, Generalized wavelet quasilinearization method for solving population growth model of fractional order, Mathematical Methods in the Applied Sciences, 43 (2020), 8753-8762.
  • [29] G. Swaminathan, G. Hariharan, V. Selvaganesan, and S. Bharatwaja, A new spectral collocation method for solving Bratutype equations using Genocchi polynomials, Journal of Mathematical Chemistry, (2021).
  • [30] H. Tajadodi, Efficient technique for solving variable order fractional optimal control problems, Alex. Eng. J., 59, (2020), 5179–5185.
  • [31] I. Talib and F. Özger, Orthogonal polynomials based operational matrices with applications to bagleytorvik fractional derivative differential equations, IntechOpen, (2023).
  • [32] I. Talib and M. Bohner, Numerical study of generalized modified caputo fractional differential equations, International Journal of Computer Mathematics, 100 (2023), 153–176.
  • [33] I. Talib, A. N. Zulfiqar, Z. Hammouch, and H. Khalil, Compatibility of the Paraskevopouloss algorithm with operational matrices of VietaLucas polynomials and applications, Mathematics and Computers in Simulation, 202 (2022), 442–463.
  • [34] I. Talib, A. Raza, A. Atangana, and M. B. Riaz, Numerical study of multi-order fractional differential equations with constant and variable coefficients, Journal of Taibah University for Science, 16 (2022), 608–620.
  • [35] I. Talib, N. Alam, D. Baleanu, and D. Zaidi, decomposition algorithm coupled with operational matrices approach with applications to fractional differential equations, Thermal Science, 25 (2021), 449–455.
  • [36] K. G. TeBeest, Numerical and analytical solutions of Volterras population model, SIAM Rev, 39 (1997), 484–493.
  • [37] O. Tunç and C. Tunç, Solution estimates to Caputo proportional fractional derivative delay integrodifferential equations, Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Mat. RACSAM, 117 (2023).
  • [38] C. Tunç and O. Tunç, A note on the qualitative analysis of Volterra integro-differential equations, Journal of Taibah University for Science, 13 (2019), 490–496.
  • [39] Ş. Yüzbaş, A numerical approximation for Volterras population growth model with fractional order, Applied Mathematical Modelling, 37 (2013), 3216–3227.
  • [40] Ş. Yüzbaş, Improved Bessel collocation method for linear Volterra integro-differential equations with piecewise intervals and application of a Volterra population model, Applied Mathematical Modelling, 40 (2016), 5349–5363.
  • [41] Ş. Yüzbaş, M. Sezer, and B. Kemanc, Numerical solutions of integro-differential equations and application of a population model with an improved Legendre method, Applied Mathematical Modelling 37 (2013), 2086–2101.
 

آمار
تعداد مشاهده مقاله: 628
تعداد دریافت فایل اصل مقاله: 721


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب