Numerical solution of non-linear elliptic partial differential equations by successively converging successive substitution techniques

The governing differential equations are examined, taking into account the development of differential equations of motion and the boundary conditions. The development of suitable approaches for solving the elliptic partial differential equations for axisymmetric flows numerically is considered. A procedure, called the method of successive convergence, was finally developed to overcome instability problems connected with earlier methods. Attention is given to substitution formula, aspects of stability and convergence, the conditions for convergence, and details regarding the method of successive convergence.