Implementing Jacobi's method is rather simple. We start with an initial guess for \( u_{i,j}^{(0)} \) where all values are known. To obtain a new solution we solve Eq. (17) or Eq. (18) in order to obtain a new solution \( u_{i,j}^{(1)} \). Most likely this solution will not be a solution to Eq. (17). This solution is in turn used to obtain a new and improved \( u_{i,j}^{(2)} \). We continue this process till we obtain a result which satisfies some specific convergence criterion.