Compact ADI method for (2+1) dimensional parabolic PDEs

In this paper, (2+1) dimensional parabolic equations are studied by compact Alternating Direction Implicit (ADI) method. In this method, second order spatial derivatives are approximated by the standard fourth order compact finite difference formula. ADI scheme is applied to split the time step into two fractional steps. Stability of the method is clearly addressed. Numerical results are presented to demonstrate the validity and reliability of the method and results are compared with those of traditional finite difference method.