Solving inverse Huxley problem using a combined numerical method and improved teaching–learning-based optimization algorithm

Aliyari Boroujeni, Ahmad; Pourgholi, Reza; Tabasi, Seyed Hashem

doi:10.22075/ijnaa.2025.34641.5181

Solving inverse Huxley problem using a combined numerical method and improved teaching–learning-based optimization algorithm

Articles in Press

Document Type : Research Paper

Authors

Ahmad Aliyari Boroujeni ¹

Reza Pourgholi ²

Seyed Hashem Tabasi ³

¹ Department of Mathematics and Computer Science, Faculty of Sciences, University of Zanjan, 45371-38791, Zanjan, Iran

² School of Mathematics and Computer Science, Damghan University, 36715-364, Damghan, Iran

³ Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

10.22075/ijnaa.2025.34641.5181

Abstract

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.

Keywords

Inverse problems

Huxley equation

ITLBO algorithm

Numerical method

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