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Fifth step block method and shooting constant for third order nonlinear dynamical systems

Author

Listed:
  • Saumya Ranjan Jena

    (KIIT Deemed to Be University)

  • Itishree Sahu

    (KIIT Deemed to Be University)

  • Arjun Kumar Paul

    (KIIT Deemed to Be University)

Abstract

In this paper, the approximate solution of a set of nonlinear third order differential equations with mixed boundary conditions is obtained by employing the fifth step block method and Modified Taylor Series Scheme (MTSS). The motivation of this subject to implement MTSS for determining the shooting constants associated with the Initial Value Problems (IVPs) rather than Boundary Value Problems (BVPs). The fifth step block method is also used to solve nonlinear third Order Differential Equations (ODEs) on the definite interval. Two numerical examples are experimented to demonstrate the efficiency and accuracy of the proposed scheme by obtaining the absolute errors. Furhter, the order, convergence and stability of the proposed method are discussed to strengthen the theoretical concept.

Suggested Citation

  • Saumya Ranjan Jena & Itishree Sahu & Arjun Kumar Paul, 2024. "Fifth step block method and shooting constant for third order nonlinear dynamical systems," 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. 15(6), pages 2218-2229, June.
    • Handle: RePEc:spr:ijsaem:v:15:y:2024:i:6:d:10.1007_s13198-023-02237-z
    DOI: 10.1007/s13198-023-02237-z
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    Cited by:

    1. Deependra Kumar Mishra & V. Mukherjee & Bindeshwar Singh, 2024. "Distributed generations planning in distribution networks using genetic algorithm-based multi-objective optimization," 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. 15(11), pages 5246-5264, November.

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