[1] H. D. Mazraeh and K. Parand, An innovative combination of deep q-networks and context-free grammars for symbolic solutions to differential equations, 142, 109733, (2025).
[2] H. D. Mazraeh, K. Parand, M. Hosseinzadeh, J. Lansky, and V. Nulícek, An improved water strider algorithm for solving the inverse burgers huxley equation, Scientific Reports, (2024).
[3] A. H. Hasanoglu and V. G. Romanov, Introduction to Inverse Problems for Differential Equations. Springer Cham, 2017.
[4] R. Pourgholi, H. Dana, and S. H. Tabasi, Solving an inverse heat conduction problem using genetic algorithm: Sequential and multi-core parallelization approach, Applied Mathematical Modelling, 38(7), 1948–1958, (2014).
[5] H. W. Engl, M. Hanke, and A. Neubauer, Regularization of inverse problems, vol. 375. Springer Science & Business Media, 1996.
[6] Ü. Lepik, Solving pdes with the aid of two-dimensional haar wavelets, Computers & Mathematics with Applications, 61(7), 1873–1879, (2011).
[7] S. Dong and Y. Wang, A method for computing inverse parametric pde problems with random-weight neural networks, 489, 112263, (2023).
[8] R. J. LeVeque, Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems. SIAM, 2007.
[9] S. C. Brenner, The mathematical theory of finite element methods. Springer, 2008.
[10] M. Raissi, P. Perdikaris, and G. Karniadakis, Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, 378, 686–707, (2019).
[11] G. E. Karniadakis, I. G. Kevrekidis, L. Lu, P. Perdikaris, S. Wang, and L. Yang, Physics-informed machine learning, Nature Reviews Physics, 3(6), 422–440, (2021).
[12] Y. Chen, Y. Luo, Q. Liu, H. Xu, and D. Zhang, Symbolic genetic algorithm for discovering open-form partial differential equations (sga-pde), Physical Review Research, 4(2), 023174, (2022).
[13] T. T. N. Nguyen, Bi-level iterative regularization for inverse problems in nonlinear pdes, Inverse Problems, 40(4), 045020, (2024).
[14] H. Dana Mazraeh, K. Parand, H. Farahani, and S. R. Kheradpisheh, An improved imperialist competitive algorithm for solving an inverse form of the huxley equation, Iranian Journal of Numerical Analysis and Optimization, 14(3), 681–707, (2024).
[15] R. Rajabioun, Cuckoo optimization algorithm, Applied Soft Computing, 11(8), 5508–5518, (2011).
[16] X.-S. Yang, Cuckoo search for inverse problems and simulated-driven shape optimization, Journal of Computational Methods in Science and Engineering, 12(1-2), 129–137, (2012).
[17] S. Pakravan, P. A. Mistani, M. A. Aragon-Calvo, and F. Gibou, Solving inverse-pde problems with physics-aware neural networks, 440, 110414, (2021).
[18] J. Ross, A. F. Villaverde, J. R. Banga, S. Vázquez, and F. Morán, A generalized fisher equation and its utility in chemical kinetics, Proceedings of the National Academy of Sciences, 107(29), 12777–12781, (2010).
[19] J. J. Bramburger and C. Henderson, The speed of traveling waves in a fkpp-burgers system, Archive for Rational Mechanics and Analysis, 241(2), 643–681, (2021).
[20] A.-M. Wazwaz, The tanh method for generalized forms of nonlinear heat conduction and burgers–fisher equations, Applied Mathematics and Computation, 169(1), 321–338, (2005).
[21] 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, Computational and Applied Mathematics, 42(2), 99, (2023).
[22] N. A. Kudryashov, Exact solutions of a family of fisher equations, Theoretical and Mathematical Physics, 94(2), 211–218, (1993).
[23] X. Wang and Y. Lu, Exact solutions of the extended burgers-fisher equation, Chin. Phys. Lett., 7(4), 145–147, (1990).
[24] M. El-Hachem, S. W. McCue, W. Jin, Y. Du, and M. J. Simpson, Revisiting the fisher–kolmogorov–petrovsky–piskunov equation to interpret the spreading–extinction dichotomy, Proceedings of the Royal Society A, 475(2229), 20190378, (2019).
[25] A. P. Márquez, R. de la Rosa, T. M. Garrido, and M. L. Gandarias, Conservation laws and exact solutions for time-delayed burgers–fisher equations, Mathematics, 11(17), 3640, (2023).
[26] T. Tang, L.-L. Wang, H. Yuan, and T. Zhou, Rational spectral methods for pdes involving fractional laplacian in unbounded domains, SIAM Journal on Scientific Computing, 42(2), A585–A611, (2020).
[27] C. Sheng, D. Cao, and J. Shen, Efficient spectral methods for pdes with spectral fractional laplacian, Journal of Scientific Computing, 88(1), 4, (2021).
[28] J. P. Boyd, Chebyshev and Fourier spectral methods. Courier Corporation, 2001.
[29] G. G. Tejani, N. Mashru, P. Patel, S. K. Sharma, and E. Celik, Application of the 2-archive multi-objective cuckoo search algorithm for structure optimization, Scientific Reports, 14(1), 31553, (2024).
[30] X.-S. Yang and S. Deb, Engineering optimisation by cuckoo search, International Journal of Mathematical Modelling and Numerical Optimisation, 1(4), 330–343, (2010).
[31] E. Shadkam and M. Bijari, Evaluation the efficiency of cuckoo optimization algorithm, arXiv preprint arXiv:1405.2168, (2014).
[32] A. H. Gandomi, X.-S. Yang, and A. H. Alavi, Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems, 29, 17–35, (2013).