MATLAB Script File for Solving Heat Transfer Equation Using Explicit Difference Method

This article provides the following content: A MATLAB script file implementing the explicit difference method for solving heat transfer equations with plotting capabilities, complete with detailed explanations and guaranteed solution stability. The implementation includes proper handling of stability conditions through Courant-Friedrichs-Lewy (CFL) criteria validation. We will provide detailed explanations of the physical significance of the solutions, including temperature distribution analysis and boundary condition handling. Additionally, we will explore different numerical methods and compare their advantages and disadvantages, focusing on computational efficiency and accuracy trade-offs. The script incorporates matrix operations for efficient computation and uses MATLAB's visualization tools for result presentation. Finally, we will demonstrate practical applications of this script through solved examples, including heat conduction in various materials and transient thermal analysis scenarios. The code includes error checking and validation routines to ensure reliable numerical results.