In nowadays, it is still a challenge to solve electrically large problems using numerical methods, although the computing power is increasing continuously. Finite difference techniques have been widely used to solve many electromagnetic problems. These methods utilize the Yee cell to discretize the computational domain. The standard Yee scheme used in Finite Difference Frequency Domain (FDFD) method is only second-order accurate. In this study, fourth-and sixth-order accurate FDFD schemes are proposed. One of the most important aspects of FDFD methods is flexibility. Each cell can have a permittivity, permeability and other material parameters independent of others. Therefore it is easy to apply to non-uniform media. The fundamental performances of the proposed methods such as accuracy and memory requirement are presented and compared to the multiresolution frequency domain (MRFD), standard FDFD schemes and analytical solutions through several numerical examples. FDFD(4) method provides 63% and 92% efficiency compared to MRFD and FDFD(2) respectively. The matrix fill ratio for circular and square cylinder samples are achieved as 0.0094% and 0.0132% correspondingly.