MATLAB-based Finite Difference Method for Electrostatic Field Numerical Analysis

This is a MATLAB-based numerical analysis program for electrostatic fields, primarily designed to solve electric field distribution problems. The program implements the finite difference method (FDM), which is one of the most widely used numerical computation techniques for converting continuous mathematical models into discrete difference equations. The core algorithm involves discretizing Poisson's equation using central difference schemes on a grid structure, typically implemented through matrix operations and iterative solvers like Gauss-Seidel or successive over-relaxation (SOR) methods. The code structure includes boundary condition handling, potential field calculation, and electric field derivation from gradient operations. Additionally, the program incorporates data visualization capabilities using MATLAB's graphical functions (such as contour, quiver, and surf plots) to display electric field distributions as 2D/3D images, enabling users to intuitively analyze and interpret field patterns, potential gradients, and charge distributions. The implementation supports customizable grid resolution, dielectric material properties, and various electrode configurations through parameter modification in the script.