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Link to original content: https://doi.org/10.1007/s13198-023-02237-z
Fifth step block method and shooting constant for third order nonlinear dynamical systems | International Journal of System Assurance Engineering and Management Skip to main content
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Fifth step block method and shooting constant for third order nonlinear dynamical systems

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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.

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  1. Department of Mathematics, School of Applied Sciences, KIIT Deemed to Be University, Bhubaneswar, Odisha, 751024, India

    Saumya Ranjan Jena, Itishree Sahu & Arjun Kumar Paul

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  1. Saumya Ranjan Jena
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  2. Itishree Sahu
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  3. Arjun Kumar Paul
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All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by SRJ. IS. AKP. All authors read and approved the final manuscript.

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Correspondence to Saumya Ranjan Jena.

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Jena, S.R., Sahu, I. & Paul, A.K. Fifth step block method and shooting constant for third order nonlinear dynamical systems. Int J Syst Assur Eng Manag 15, 2218–2229 (2024). https://doi.org/10.1007/s13198-023-02237-z

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