Centered finite difference is the basic method in this paper for spatial discretization. In general, except the schemes that will be used adjacent tothe boundary points, centered finite difference schemes will be used on the main mesh points. Depending on the requirement of order of accuracy and optimization, different multi-point stencil schemes will be built in Matlab in the form of matrix. As a result, solving PDEs is actually operating matrices in Matlab. Standard schemes and optimized schemeswill be tested with 1D linear convection equation before applying them to the solvers. In 2D-pulse case, the rectangular domain will be transformed into a wavy domain and as a result Jacobian transformation method will betested. Results from different schemes will be compared with the analytical solution in two dimensional pulse case.