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To improve the accuracy of the scheme we replace (3) by an implicit scheme to produce a more w e consider fourth order accurate compact accurate scheme. We approximate the spatial schemes for numerical solutions to the Maxwell derivatives to fourth order, using the following im.equations. We use the same mesh stencil as Used plicit method for $f: in the standard Yee scheme. In particular extra ~( 2 , 4 ) : information over a wider stencil is not required. Hence, it is relatively easy to modify an existing code based on the Yee algorithm to make it (4) fourth order accurate. Also, a staggered mesh AY makes the boundary treatment easier. Finally, a staggered grid system gives a lower error than a non-staggered system. Finite Differences SchemeThe normalized TM wave equations are: aEz aHy a H , at ax ay aH, aE, at ay aff, -aEz at a x that will enable us to generalize it easily. -(1) -----We present Yee's difference equation in a form +i[(E) 24 i,j+3/2 +(") ay i,j-l/2 ] We refer to (3) as the Yee scheme and (4) as the Ty scheme. We shall use. second and fourth order accurate time discretizations for the Ty scheme. Equation (4) requires the inversion of a tridiagonal matrix for ( $ f ) , , J .We stress that the only difference between the Yee scheme and the (2,4) scheme is the replacement of (3) by (4). Thus, the scheme is fourth order in space but only second order in time. This is reasonable since we can improve the temporal accuracy by choosing a smaller time step. This increases the work only linearly and does not increase the storage. A fourth order scheme in space enables us to choose a coarser mesh. This decreases the work in each space dimension and also decreases the storage. Hence, the accuracy in space is of greater importance then the accuracy in time.where Yee:At the first and last points we use a fourth order accurate one sided appropximation to the derivative. We note that this is used only in order to globally approximate the derivative. No physical boundary conditions are included at this stage. w,, = Ut+1/2,1 -u,-1/2,3