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An analytical solution to Yee's FDTD partial difference equations for a one-dimensional cavity problem via z-transform

An analytical solution to the Yee's FDTD partial difference equations via z-transform has been presented and compared with the exact continuous wave solution for a one-dimensional cavity problem. Both results are in a similar form and the inherent errors of the Yee scheme have been identified. The obtained solution has also been verified with the direct implementation of the Yee scheme.