Cubature method for the numerical solution of the characteristic initial value problem

Abstract

The resemblance of the Goursat problem for the hyperbolic partial differential equations to the initial value problem for the ordinary differential equations has suggested the extension of many well known numerical methods existing for (1.2) to the numerical treatment of (1.1). Day [2] discusses the quadrature methods while Diaz [3] generalizes the simple Euler-method. Moore [6] gives an analogue to the fourth order Runge-Kutta-method and Tornig [7] generalizes the explicit and implicit Adams-methods.