when applying the method of Finite Difference Time domain(FDTD)technique combined with Thompson transformation to calculate electromagnetic scattering problems of complex objects^[1],the selection of difference schemes has an effect directly on the accuracy of numerical solution.In this paper,a new difference scheme with high order accuracy is presented,numerical results show that Thompson FDTD method can accurately calculate the electromagnetic scattering problems of arbitrary targets.

Using the series expansion and the iterative multinomial expansion of the characteristic values of the Mathieu functions,Mathieu functions and its addition theorem are evaluated numerically.Calculated results are in largely conformity with the reference [1],and the precision appears an accuracy of better than 10^-5 in the range r≤30 and 0≤ q≤ 50.