On the numerical solution of the Goursat problem

摘要

In this paper, we present a nonlinear trapezoidal formula for the solution of the Goursat problem. The new scheme implements the harmonic mean (HM) averaging of the functional values rather than the arithmetic mean (AM) or the geometric mean (GM) averaging. A comparison is made with the existing techniques, and the results obtained show better approximations related to the accuracy level in favor of the HM strategy.