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A new hybrid method of Evolutionary-Numerical algorithms to solve ODEs arising in physics and engineering

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Abstract

The present study aimed to use artificial intelligence to obtain a mathematical model to approximate the exact solution for linear and nonlinear ordinary differential equations with initial conditions arising in physics and engineering. To this end, genetic programming has been implemented, along with its combination with the Runge–Kutta fourth order method (RK4). Regarding formulation, the produced mathematical models by this new hybrid method (GPN) are flexible (in terms of functions used in the model structure and the number of them) and have acceptable accuracy compared to other existing traditional powerful methods now in use. Numerical experiments have been adequately conducted to indicate the sufficient accuracy and productive power of GPN to generate human-competitive results.

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Authors and Affiliations

  1. Department of Applied Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran

    S. R. Mirshafaei, H. Saberi Najafi & A. H. Refahi Sheikhani

  2. Department of Dynamic, Control, and Vibration, Faculty of Mechanical Engineering, University of Guilan, Rasht, Iran

    E. khaleghi

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  1. S. R. Mirshafaei
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Mirshafaei, S.R., Najafi, H.S., khaleghi, E. et al. A new hybrid method of Evolutionary-Numerical algorithms to solve ODEs arising in physics and engineering. Genet Program Evolvable Mach 24, 1 (2023). https://doi.org/10.1007/s10710-023-09450-6

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