On difference methods for the Darboux problem for an equation of mixed hyperbolic-parabolic type

AbstractWe derive an a priori estimate for a finite difference scheme for a second order hyperbolic equation with variable coefficients. The equation is allowed to degenerate to a parabolic equation on the x-axis. The mesh region consists of points of intersection of the characteristic curves drawn from points on the x-axis. Uniqueness and existence of the solution to the discrete version of the Darboux (Goursat) problem and convergence of the numerical solution to the exact solution follow directly from this estimate