Uniform convergence with orderh 4 of a scheme of the method of lines for quasilinear parabolic and hyperbolic equations

The order of uniform convergence of the method of lines is considered in connection with the solution of the first boundary-value problem for quasilinear second-order parabolic and hyperbolic equations.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 48, pp. 205–211, 1974.