MATLAB-Based Learning of Simultaneous Linear Equation Systems

Abstract

Problems involving mathematical models are commonly found across various scientific disciplines, such as physics, chemistry, biology, economics, and engineering. These mathematical models are used to represent complex real-world phenomena in order to analyze and understand them quantitatively. However, in practice, these models often take the form of complex, nonlinear, or high-dimensional equation systems, which are not easily solved using standard analytical methods or conventional algebraic formulas. To overcome these limitations, numerical methods are employed as an alternative approach. Numerical methods provide solutions to mathematical problems by relying on computational techniques and iterative procedures. One of the key topics within numerical methods is the solution of Simultaneous Linear Equation Systems (SLES), which frequently arise in practical applications such as structural analysis, fluid dynamics, and economic modeling including structural assessment, flow dynamics, and economic forecasting. Solving these systems often requires a large number of iterative calculations, making manual computation inefficient and time-consuming. Therefore, the use of computational software such as MATLAB becomes essential in both learning and applying these methods. MATLAB provides a broad array of functions and numerical tools this significantly support an  efficient and accurate solution of linear equation systems. In an educational context, the use of MATLAB not only simplifies the computational process but also aids students in understanding fundamental concepts of numerical methods through visualization, simulation, and digital experimentation. Thus, integrating MATLAB into the learning process of numerical methods greatly enhances teaching and learning effectiveness, while also strengthening students' computational skills in solving real-world scientific and engineering problems.