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

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, wit...

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Vydáno v:Mathematics (Basel) Ročník 9; číslo 9; s. 920
Hlavní autoři: Ogbonnaya, Chukwuma, Abeykoon, Chamil, Nasser, Adel, Turan, Ali
Médium: Journal Article
Jazyk:angličtina
Vydáno: Basel MDPI AG 01.05.2021
Témata:
Algorithms
code-based modelling approach
Codes
computational solutions
Cooling
Decomposition
Engineering
Food science
Independent variables
Mathematical models
numerical analysis
Numerical models
photovoltaics
Robustness (mathematics)
Scientists
Simultaneous equations
Sine-Gordon equations
Software
system of transcendental equation
Transcendental functions
Trigonometric functions
Variables
Wave functions
ISSN:2227-7390, 2227-7390
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Shrnutí: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 x1 = 1:0.0005:100 to x1 = 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.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math9090920