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A Computational Approach to Solve a System of Transcendental Equations with Multi-Functions and Multi-Variables

Author

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  • Chukwuma Ogbonnaya

    (Department of Mechanical, Aerospace and Civil Engineering, The University of Manchester, Manchester M13 9PL, UK
    Faculty of Engineering and Technology, Alex Ekwueme Federal University, Ndufu Alike Ikwo, Abakaliki PMB 1010, Nigeria)

  • Chamil Abeykoon

    (Aerospace Research Institute and Northwest Composites Centre, School of Materials, The University of Manchester, Manchester M13 9PL, UK)

  • Adel Nasser

    (Department of Mechanical, Aerospace and Civil Engineering, The University of Manchester, Manchester M13 9PL, UK)

  • Ali Turan

    (Independent Researcher, Manchester M22 4ES, Lancashire, UK)

Abstract

A system of transcendental equations (SoTE) is a set of simultaneous equations containing at least a transcendental function. Solutions involving transcendental equations are often problematic, particularly in the form of a system of equations. This challenge has limited the number of equations, with inter-related multi-functions and multi-variables, often included in the mathematical modelling of physical systems during problem formulation. Here, we presented detailed steps for using a code-based modelling approach for solving SoTEs that may be encountered in science and engineering problems. A SoTE comprising six functions, including Sine-Gordon wave functions, was used to illustrate the steps. Parametric studies were performed to visualize how a change in the variables affected the superposition of the waves as the independent variable varies from x 1 = 1:0.0005:100 to x 1 = 1:5:100. The application of the proposed approach in modelling and simulation of photovoltaic and thermophotovoltaic systems were also highlighted. Overall, solutions to SoTEs present new opportunities for including more functions and variables in numerical models of systems, which will ultimately lead to a more robust representation of physical systems.

Suggested Citation

  • Chukwuma Ogbonnaya & Chamil Abeykoon & Adel Nasser & Ali Turan, 2021. "A Computational Approach to Solve a System of Transcendental Equations with Multi-Functions and Multi-Variables," Mathematics, MDPI, vol. 9(9), pages 1-13, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:920-:d:540122
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    References listed on IDEAS

    as
    1. Porubov, A.V. & Fradkov, A.L. & Andrievsky, B.R., 2015. "Feedback control for some solutions of the sine-Gordon equation," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 17-22.
    2. Sun, Yunchuan, 2015. "New exact traveling wave solutions for double Sine–Gordon equation," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 100-104.
    3. Chukwuma Ogbonnaya & Chamil Abeykoon & Adel Nasser & Ali Turan, 2020. "Radiation-Thermodynamic Modelling and Simulating the Core of a Thermophotovoltaic System," Energies, MDPI, vol. 13(22), pages 1-15, November.
    Full references (including those not matched with items on IDEAS)

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