Many nonlinear problems that arise in various science and engineering fields can be
modelled by the Goursat partial differential equations. Modelling these non-linear
problems using the Goursat partial differential equations has not received much
attention especially the theoretical aspect . The proposed scheme of solution is
supported by examining a nonlinear Goursat problem. The verification of the
theoretical results from several series of numerical experiments are discussed. Results
obtained from Taylor series expansion show that the proposed new scheme is
consistent. By using the von Neumann analysis and essence of stability, the proposed
new scheme is found to be unconditionally stable. In addition, the trend of the
numerical results shows that the new scheme is also convergent.