First, I would like to express my sincere gratitude to my supervisor, Assoc. Prof. Tan Eng Leong, for introducing me to the fascinating area of unconditionally stable finite-difference time-domain methods, and also for his guidance throughout my Ph.D. candidature. The completion of this thesis would not have been possible without his valuable advice and motivation. I would like to thank DSO National Laboratories, Singapore for the scholarship provided. I would also like to thank the faculty and laboratory staffs at the School of Electrical and Electronic Engineering for their support and assistance. Last but not least, I am sincerely grateful to my parents and family members for their encouragement and understanding.