  In this paper a nonlinear Euler-Poisson-Darboux system is considered. In a
first part, we proved the genericity of the hypergeometric functions in the
development of exact solutions for such a system in some special cases leading
to Bessel type differential equations. Next, a finite difference schemle in
two-dimensional case has been developed. The continuous system is transformed
into an algebraic quasi linear discrete one leading to generalized
Lyapunov-Sylvester operators. The discrete algebraic system is proved to be
uniquely solvable, stable and convergent based on Lyapunov criterion of
stability and Lax-Richtmyer equivalence theorem for the convergence. A
numerical example has been provided at the end to illustrate the efficiency of
the theoretical results. The present method is thus proved to be more accurate
than existing ones and lead to faster algorithms.
