Compact Schemes for the Spatial Discretization of Linear Elliptic Partial Differential Equations

A system of compact schemes used, to approximate the partial derivative 2 2 1 f x   and 2 2 2 f x   of Linear Elliptic Partial Differential Equations (LEPDE) ,on the non-boundary nodes, located along a particular horizontal grid line for 2 2 1 f x   and along a particular vertical grid line for 2 2 2 f x   of a two-dimensional structured Cartesian uniform grid. The aim of the numerical experiment is to demonstrate the higher order spatial accuracy and better rate of convergence of the solution, produced using the developed compact scheme. Further, these solutions are compared with the same, produced using the conventional 2 nd order scheme. The comparison is made, in terms of the discrete l l 2 &  norms, of the true error. The true error is defined as, the difference between the computed numerical and the available exact solution, of the chosen test problems. It is computed on every non-boundary node bounded in the computational domain.