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

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Department of Mechanical, Aerospace and Civil Engineering, The University of Manchester, Manchester M13 9PL, UK
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Faculty of Engineering and Technology, Alex Ekwueme Federal University, Ndufu Alike Ikwo, Abakaliki PMB 1010, Nigeria
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Aerospace Research Institute and Northwest Composites Centre, School of Materials, The University of Manchester, Manchester M13 9PL, UK
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Independent Researcher, Manchester M22 4ES, Lancashire, UK
*
Author to whom correspondence should be addressed.
Academic Editor: Maria Luminița Scutaru
Mathematics 2021, 9(9), 920; https://doi.org/10.3390/math9090920
Received: 2 April 2021 / Revised: 17 April 2021 / Accepted: 19 April 2021 / Published: 21 April 2021
(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems)
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. View Full-Text
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MDPI and ACS Style

Ogbonnaya, C.; Abeykoon, C.; Nasser, A.; Turan, A. A Computational Approach to Solve a System of Transcendental Equations with Multi-Functions and Multi-Variables. Mathematics 2021, 9, 920. https://doi.org/10.3390/math9090920

AMA Style

Ogbonnaya C, Abeykoon C, Nasser A, Turan A. A Computational Approach to Solve a System of Transcendental Equations with Multi-Functions and Multi-Variables. Mathematics. 2021; 9(9):920. https://doi.org/10.3390/math9090920

Chicago/Turabian Style

Ogbonnaya, Chukwuma, Chamil Abeykoon, Adel Nasser, and Ali Turan. 2021. "A Computational Approach to Solve a System of Transcendental Equations with Multi-Functions and Multi-Variables" Mathematics 9, no. 9: 920. https://doi.org/10.3390/math9090920

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