Rate of convergence of discretization methods for the wave equation with generalized solutions

Exact difference scheme operators are applied to construct a method of lines scheme and a difference scheme for a multidimensional hyperbolic equation. An accuracy bound compatible with the smoothness of the solution of the differential problem is defined for the method of lines and the grid method. The accuracy of the two schemes is established in the sense of this definition. A computational experiment shows that the lower accuracy of the method of lines and the grid method for the hyperbolic equation compared with the accuracy bounds for elliptic and parabolic equations is attributable to the specific features of the hyperbolic equations.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 57, pp. 26–33, 1985.