Direct and iterative methodsIterative method of the solution of the systems of algebraic equations, to which the discretisation of partial differential transport equations leads, are described. Cramer’s ruleCramer’s rule is shown to be applicable to the solution of systems of small numbers of equations but not to the realistic systems typical to CFD calculations. The JacobiJacobi and Gauss-Seidel point-by-point methods are described as typical examples of the iterative methodsIterative method. The Gauss-Seidel point-by-point method is shown to more quickly lead to convergence of the process compared with the JacobiJacobi method. The Scarborough criterionScarborough criterion, which guarantees the convergence of the Gauss-Seidel point-by-point method, is formulated and applied to specific systems of equations. It is pointed out that the Gauss-Seidel line-by-lineGauss-Seidel line-by-line method, in which the system of equations along a specific line (e.g. from South to North) is solved directly, assuming that the values of variables along other lines are inferred from the initial guess or previous iteration, is the most efficient one for CFD applications. The equations solved in the Gauss-Seidel line-by-lineGauss-Seidel line-by-line method contain no more than three unknowns, which makes it possible to apply the Thomas algorithmThomas algorithm for their numerical solution. The latter algorithm contains two stages: forward elimination and backward substitution.