Comparative study of two and three level ADI methods for parabolic equations with a mixed derivative

ADI difference schemes of two and three levels for the parabolic equations with a mixed derivative have been derived. Using the stability analysis and the principal part of the truncation error, a difference formula with minimum truncation error has been found. Comparative study of the two and three level formulas has been made through two examples, one with constant coefficients and another with variable coefficients.