Course Design – 1D Poisson Equation (Dirichlet BC)

This repository aims to solve the one-dimensional Poisson equation with Dirichlet boundaries by iterative methods such as Jacobi, Gauss–Seidel (G-S) and SOR.

Files

• 1d.py
  A simple test program to solve the 1D discrete Poisson equation with Jacobi / G-S / SOR and plot the solution and residual convergence. (Not used directly in the report.)

• 1ddilichlet.py
  Main program to solve the 1D discrete Poisson equation with Dirichlet boundaries using Jacobi, G-S and SOR, and compare their iteration counts, errors and runtime.

• 1dSOR.py
  Example script using SOR with a fixed relaxation factor to show the numerical solution and convergence behavior.

• 1dSORomega.py
  Example script to scan different SOR relaxation factors ω and study how ω affects convergence.

• 1dSORstepsize.py
  Example script to study how the grid size (step size) influences SOR convergence and accuracy.

• 求解离散泊松方程的三种迭代方法比较.pdf
  Short report summarizing the model, the three iterative methods, and numerical comparison results.