پیوندهای مفید
آمار
| تعداد نشریات | 22 |
| تعداد شمارهها | 713 |
| تعداد مقالات | 10,261 |
| تعداد مشاهده مقاله | 72,034,471 |
| تعداد دریافت فایل اصل مقاله | 63,789,846 |
Solving inverse Huxley problem using a combined numerical method and improved teaching–learning-based optimization algorithm | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 27 خرداد 1405 اصل مقاله (722.89 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2025.34641.5181 | ||
| نویسندگان | ||
| Ahmad Aliyari Boroujeni1؛ Reza Pourgholi* 2؛ Seyed Hashem Tabasi3 | ||
| 1Department of Mathematics and Computer Science, Faculty of Sciences, University of Zanjan, 45371-38791, Zanjan, Iran | ||
| 2School of Mathematics and Computer Science, Damghan University, 36715-364, Damghan, Iran | ||
| 3Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran | ||
| تاریخ دریافت: 12 تیر 1403، تاریخ بازنگری: 25 آذر 1403، تاریخ پذیرش: 03 فروردین 1404 | ||
| چکیده | ||
| In this paper, inverse Huxley partial differential equations problem is solved using a combination of numerical methods and improved teaching–learning-based optimization (ITLBO) meta-heuristic algorithm. The ITLBO algorithm, which is a population-oriented algorithm, is very efficient for solving inverse problems by increasing the discovery capacity and diversity of input data. In the method presented in this article, by considering each input data of the ITLBO algorithm as an answer for inverse Huxley problem, the problem is solved by numerical methods. The results obtained from the implementation of the combination of the numerical method and the ITLBO algorithm show that it is possible to get accurate answers for inverse Huxley problem without guessing the function type of the inverse problem. The results also indicate that combining Implicit and Explicit numerical methods, along with the features of the ITLBO algorithm, which searches across various intervals, can lead to solving inverse problems like Huxley without considering the type of the unknown function. The exact results obtained from the implementation of the presented method were obtained on a 2.5 GHz 4-core Intel CPU. | ||
| کلیدواژهها | ||
| Inverse problems؛ Huxley equation؛ ITLBO algorithm؛ Numerical method | ||
| مراجع | ||
|
[1] A. Aliyari Boroujeni, R. Pourgholi, and S.H. Tabasi, A new improved teaching‑learning‑based optimization (ITLBO) algorithm for solving nonlinear inverse partial differential equation problems, Comp. Appl. Math. 42 (2023), 99.
[2] A. Aliyari Boroujeni, R. Pourgholi, and S.H. Tabasi, Solving inverse partial differential equations problems by using teaching learning based optimization algorithm, TWMS J. Appl. Eng. Math. (2024).
[3] A. Aliyari Boroujeni, R. Pourgholi, and S.H. Tabasi, Numerical solutions of KDV and mKDV equations: Using sequence and multi‑core parallelization implementation, J. Comput. Appl. Math. 454 (2025), 116184.
[4] R.S. Anderssen, Inverse problems: a pragmatist's approach to the recovery of information from indirect measurements, Aust. N. Z. Ind. Appl. Math. J. 46 (2005), C588‑C622.
[5] D.G. Aronson and H.F. Weinberger, Multidimensional nonlinear diffusion arising in population genetics, Adv. Math. 30 (1978), no. 1, 33‑76.
[6] E. Babolian and J. Saeidian, Analytic approximate solutions to Burgers, Fisher, Huxley equations and two combined forms of these equations, Commun. Nonlinear Sci. Numer. Simul. 14 (2009), 1984‑1992.
[7] Y. Bai, T. Chaolu, and S. Bilige, Solving Huxley equation using an improved PINN method, Nonlinear Dyn. 105 (2021), 3439‑3450.
[8] B. Batiha, M.S.M. Noorani, and I. Hashim, Numerical simulation of the generalized Huxley equation by He's variational iteration method, Appl. Math. Comput. 186 (2007), no. 2, 1322‑1325.
[9] J.V. Beck and D.C. Murio, Combined function specification‑regularization procedure for solution of inverse heat condition problem, AIAA J. 24 (1986), 180‑185.
[10] J.M.G. Cabez, J.A.M. Garcia, and A.C. Rodriguez, A sequential algorithm of inverse heat conduction problems using singular value decomposition, Int. J. Therm. Sci. 44 (2005), 235‑244.
[11] H. Dong, Y. Xu, D. Cao, W. Zhang, Z. Yang, and X. Li, An improved teaching‑learning‑based optimization algorithm with a modified learner phase and a new mutation‑restarting phase, Knowl.‑Based Syst. 258 (2022), 109989.
[12] L. Duan and Q. Lu, Bursting oscillations near codimension‑two bifurcations in the Chay Neuron model, Int. J. Nonlinear Sci. Numer. Simul. 7 (2006), no. 1, 59‑64.
[13] S. Foadian, R. Pourgholi, and S.H. Tabasi, Cubic B‑spline method for the solution of an inverse parabolic system, Appl. Anal. 97 (2017), no. 3, 438‑465.
[14] S. Foadian, R. Pourgholi, S.H. Tabasi, and J. Damirchi, The inverse solution of the coupled nonlinear reaction‑diffusion equations by the Haar wavelets, Int. J. Comput. Math. 96 (2019), no. 1, 105‑125.
[15] S. Foadian, R. Pourgholi, and A. Esfahani, Numerical solution of the linear inverse wave equation, Int. J. Nonlinear Anal. Appl. 13 (2022), no. 2, 1907‑1926.
[16] S. Foadian, R. Pourgholi, and A. Esfahani, Numerical solution of the linear inverse wave equation, Int. J. Nonlinear Anal. Appl. 13 (2022), no. 2, 1907‑1926.
[17] A.L. Hodgkin and A.F. Huxley, A Quantitative description of ion currents and its applications to conduction and excitation in nerve membranes, J. Physiol. 117 (1952), 500‑544.
[18] M. Javidi and A. Golbabai, A new domain decomposition algorithm for generalized Burger's‑Huxley equation based on Chebyshev polynomials and preconditioning, Chaos Solitons Fractals 39 (2009), no. 2, 849‑857.
[19] Z. Jiang, F. Zou, D. Chen, S. Cao, H. Liu, and W. Guo, An ensemble multi‑swarm teaching‑learning‑based optimization algorithm for function optimization and image segmentation, Appl. Soft Comput. 130 (2022), 109653.
[20] S. Liu, T. Fan, and Q. Lu, The spike order of the winnerless competition (WLC) model and its application to the inhibition neural system, Int. J. Nonlinear Sci. Numer. Simul. 6 (2005), no. 2, 133‑138.
[21] L.B. Liu, Y. Liang, J. Zhang, and X. Bao, A robust adaptive grid method for singularly perturbed Burger‑Huxley equations, Electron. Res. Arch. 28 (2020), no. 4, 1439‑1457.
[22] R. Mohammadi, B‑spline collocation algorithm for numerical solution of the generalized Burger's‑Huxley equation, Numer. Methods Partial Differ. Equ. 29 (2013), no. 4, 1173‑1191.
[23] R.K. Mohanty, W. Dai, and D. Liu, Operator compact method of accuracy two in time and four in space for the solution of time dependent Burgers‑Huxley equation, Numer. Algorithms 70 (2015), no. 3, 591‑605.
[24] R. Pourgholi, S.H. Tabasi, and H. Zeidabadi, Numerical techniques for solving system of nonlinear inverse problem, Eng. Comput. 34 (2018), 487‑502.
[25] R.V. Rao, V.J. Savsani, and D.P. Vakharia, Teaching‑learning‑based optimization: a novel method for constrained mechanical design optimization problems, Comput.‑Aided Des. 43 (2011), 303‑315.
[26] R.V. Rao, V.J. Savsani, and D.P. Vakharia, Teaching learning‑based optimization: an optimization method for continuous non‑linear large scale problems, Inf. Sci. 183 (2012), 1‑15.
[27] R.V. Rao and V. Patel, An improved teaching‑learning‑based optimization algorithm for solving unconstrained optimization problems, Sci. Iran. 20 (2013), no. 3, 710‑720.
[28] A. Saeedi, S. Foadian, and R. Pourgholi, Applications of two numerical methods for solving inverse Benjamin‑Bona‑Mahony‑Burgers equation, Eng. Comput. 36 (2020), no. 4, 1453‑1466.
[29] C.W. Sahabandu, D. Karunarathna, P. Sewvandi, et al., A method of directly defining the inverse mapping for a nonlinear partial differential equation and for systems of nonlinear partial differential equations, Comput. Appl. Math. 40 (2021), 234.
[30] J. Satsuma, Exact Solutions of Burgers' Equation with Reaction Terms, in Topics in Soliton Theory and Exact Solvable Nonlinear Equations, 1987.
[31] G.D. Smith, Numerical Solution of Partial Differential Equations, Oxford University Press, New York, 1965.
[32] X.Y. Wang, Z.S. Zhu, and Y.K. Lu, Solitary wave solutions of the generalised Burgers‑Huxley equation, J. Phys. A: Math. Gen. 23 (1990), no. 3, 271‑274.
[33] A.M. Wazwaz, Travelling wave solutions of generalized forms of Burgers, Burgers‑KdV and Burgers‑Huxley equations, Appl. Math. Comput. 169 (2005), no. 1, 639‑656.
[34] G.J. Zhang, J.X. Xu, H. Yao, and R.X. Wei, Mechanism of bifurcation‑dependent coherence resonance of an excitable neuron model, Int. J. Nonlinear Sci. Numer. Simul. 7 (2006), no. 4, 447‑450. | ||
|
آمار تعداد مشاهده مقاله: 47 تعداد دریافت فایل اصل مقاله: 36 |
||