Computational Physics Lectures: Partial differential equations

 

 

 

Jacobi Algorithm for solving Laplace's Equation, the algorithm

Summarized, this algorithm reads
  1. Make an initial guess for \( u_{i,j} \) at all interior points \( (i,j) \) for all \( i=1:n \) and \( j=1:n \)
  2. Use Eq. (17) to compute \( u^{m} \) at all interior points \( (i,j) \). The index \( m \) stands for iteration number \( m \).
  3. Stop if prescribed convergence threshold is reached, otherwise continue to the next step.
  4. Update the new value of \( u \) for the given iteration
  5. Go to step 2