Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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OPTIMAL STRATEGIES IN BIOECONOMIC DIFFERENTIAL GAMES: INSIGHTS FROM CHEBYSHEV TAU METHOD

  • Shahd H. Alkharaz (Department of Mathematics, Faculty of Science, Ain Shams University) ;
  • Essam El-Siedy (Pure Mathematics, Mathematics Department, Faculty of Science, Ain Shams University) ;
  • Eliwa M. Roushdy (Department of Basic and Applied Sciences, Arab Academy for Science, Technology and Maritime Transport) ;
  • Muner M. Abou Hasan (School of Mathematics and data science, Emirates aviation university)
  • Received : 2023.10.08
  • Accepted : 2023.11.26
  • Published : 2024.06.15
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Abstract

In the realm of differential games and bioeconomic modeling, where intricate systems and multifaceted interactions abound, we explore the precision and efficiency of the Chebyshev Tau method (CTM). We begin with the Weierstrass Approximation Theorem, employing Chebyshev polynomials to pave the way for solving intricate bioeconomic differential games. Our case study revolves around a three-player bioeconomic differential game, unveiling a unique open-loop Nash equilibrium using Hamiltonians and the FilippovCesari existence theorem. We then transition to numerical implementation, employing CTM to resolve a Three-Point Boundary Value Problem (TPBVP) with varying degrees of approximation.

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References

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