On Difference Methods for Parabolic Equations and Alternating Direction Implicit Methods for Elliptic Equations

Some aspects are discussed of the development of the theory of difference approximations to parabolic equations in its relation to the basic development of difference methods for hyperbolic and elliptic equations by Courant, Friedrichs and Lewy, [Math. Ann. 100, 32 (1928)]. The present paper also deals with the related problem of establishing the convergence of alternating direction implicit methods for elliptic problems.