Abstract
The finite- difference method is one of the most widely applied methods for the approximation of ordinary and partial differential equations. We can practice this discretization method in many science applications such as in dynamical meteorology, aerodynamic, mathematical physics, oceanography, and many other disciplines. Therefore, the convergence analysis and the error estimation of this scheme hold practical, as well as theoretical importance. When analyzing the error estimation and the convergence of the applied finite-difference scheme, the determination of the order of accuracy by the suggested scheme is important. Moreover, with investigation of the scheme, it might be possible to structure schemes with increased accuracy.