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Solving Singular Two-Point Boundary Value Problems Using Continuous Genetic Algorithm

Author

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  • Omar Abu Arqub
  • Zaer Abo-Hammour
  • Shaher Momani
  • Nabil Shawagfeh

Abstract

In this paper, the continuous genetic algorithm is applied for the solution of singular two-point boundary value problems, where smooth solution curves are used throughout the evolution of the algorithm to obtain the required nodal values. The proposed technique might be considered as a variation of the finite difference method in the sense that each of the derivatives is replaced by an appropriate difference quotient approximation. This novel approach possesses main advantages; it can be applied without any limitation on the nature of the problem, the type of singularity, and the number of mesh points. Numerical examples are included to demonstrate the accuracy, applicability, and generality of the presented technique. The results reveal that the algorithm is very effective, straightforward, and simple.

Suggested Citation

  • Omar Abu Arqub & Zaer Abo-Hammour & Shaher Momani & Nabil Shawagfeh, 2012. "Solving Singular Two-Point Boundary Value Problems Using Continuous Genetic Algorithm," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-25, November.
    • Handle: RePEc:hin:jnlaaa:205391
    DOI: 10.1155/2012/205391
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    Cited by:

    1. Lenin Kanagasabai, 2022. "Buoyancy based optimization algorithm for real power loss diminution," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(5), pages 2442-2457, October.
    2. Chaudhary, Naveed Ishtiaq & Raja, Muhammad Asif Zahoor & Khan, Zeshan Aslam & Mehmood, Ammara & Shah, Syed Muslim, 2022. "Design of fractional hierarchical gradient descent algorithm for parameter estimation of nonlinear control autoregressive systems," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    3. Khan, Zeshan Aslam & Chaudhary, Naveed Ishtiaq & Raja, Muhammad Asif Zahoor, 2022. "Generalized fractional strategy for recommender systems with chaotic ratings behavior," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    4. Muhammad, Yasir & Khan, Nusrat & Awan, Saeed Ehsan & Raja, Muhammad Asif Zahoor & Chaudhary, Naveed Ishtiaq & Kiani, Adiqa Kausar & Ullah, Farman & Shu, Chi-Min, 2022. "Fractional memetic computing paradigm for reactive power management involving wind-load chaos and uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    5. Vanalakshmi, R. & Maragathasundari, S. & Dhanalakshmi, K.S., 2022. "Queuing system in VLSI physical design," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 755-768.

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