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 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.
Highlights
The advent of the computer has made explicit solution and visualization of transcendental equations (TE) easier [1]
This study provides detailed steps on how the code-based modelling (CBM) approach can be used to solve system of transcendental equations (SoTE) with multi-functions and multi-variables
To formulate the steps, a hypothetical SoTE including Sine-Gordon equations was used to illustrate the steps for solving a SoTE
Summary
The advent of the computer has made explicit solution and visualization of transcendental equations (TE) easier [1]. The CBM approach appears to be robust in achieving numerical solutions to SoTEs, there are no clear steps for formulating and solving of scientific and engineering problems involving SoTE. The originality of this study is realized in being the first paper to present detailed steps for applying the CBM approach to facilitate numerical/computational solutions to SoTEs. the steps are proposed for problems that may be encountered in science and engineering, there is no doubt that any researcher from any field can adopt/adapt the steps. The major contribution of this paper is to demonstrate how the CBM approach can allow scientists and engineers more degrees of freedom to overcome the limitations of including multi-functions and multi-variables during model representation of physical systems involving SoTEs. Section 2 presents detailed steps for formulating SoTEs including Sine-Gordon functions.
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