Theoretical Analysis of Numerical Integration Rule for Nonlinear Goursat Problem

Abstract

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.