| Abstract: | This paper discusses a new fourth-order compact off-step discretization forthe solution of a system of two-dimensional nonlinear elliptic partial differential equationssubject to Dirichlet boundary conditions. New methods to obtain the fourth-orderaccurate numerical solution of the first order normal derivatives of the solution are alsoderived. In all cases, we use only nine grid points to compute the solution. The proposedmethods are directly applicable to singular problems and problems in polar coordinates,which is a main attraction. The convergence analysis of the derived method is discussedin detail. Several physical problems are solved to demonstrate the usefulness of the proposedmethods. |
