Alternating Direction Methods for a System of Parabolic Equations in Two Space Dimensions with a Mixed Derivative

An alternating direction (A.D.I.) method, which requires the solution of two block tridiagonal sets of equations at each time step, is suggested for solving a system of parabolic equations with variable coefficients in two space dimensions with a mixed derivative. The method is shown to be unconditionally stable for two semi-infinite ranges of an auxiliary parameter subject to restrictions on the coefficient matrices. Other existing finite difference schemes are mentioned and numerical results are pre-sented. 1