Abstract
This thesis is concerned with the application of Newton's method for multi-variable nonlinear functions to the nonlinear partial differential equation which describes two-dimensional flow of gas through porous media. | Newton's method has been shown to be general enough to be applied to other multi-dimensional nonlinear problems. It has been shown to be convergent for at least a practical range of variables and within this range has an extremely rapid rate of convergence. The results obtained from the technique compare quite favorably with other accepted techniques for solving multidimensional nonlinear problems. Finally, an approach for a priori convergence prediction is presented with suggestions for further study in this area.