A third (four)-order accurate nine-point compact EEM-FDM for coupled system of mildly non-linear elliptic equations

In this paper, we formulate a new algorithm for the approximate solution values of coupled mildly non-linear elliptic boundary value problems in two-space dimensions. The method is obtained on a non-uniformly spaced mesh points in such a manner that fourth-order accuracy of the scheme is a particular case of third-order method. The special nine-point discretization makes it easier to solve and applicable to the problems possessing layer behaviour. Applications to stationary Navier-Stokes equation and biharmonic equations have been given to illustrate the efficiency and robustness of the scheme.