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This book intends to present the basic methods for the numerical solution of hybrid differential systems in a variety of settings. These systems evolve mostly continuously in time but have formatting changes in their governing equations at a sequence of discrete times. Many authors have considered ordinary, fuzzy, stochastic, fractional, and impulsive differential equations and their extensions to hybrid systems. We focus on their numerical solution mostly by the Euler and Runge-Kutta methods, as many authors have studied and worked with more varied and specialized numerical techniques. We provide detailed proofs of the convergence of the numerical schemes which can be extended to other methods. In the Appendix we provide the Maple codes used in the text so that readers may implement their own methods of solution and obtain graphical results. We hope that the readers will extend the presented results in new directions and create applications in their scientific and technological fields involving hybrid differential equations.
Dr. Steven Pederson is an Associate Professor of Mathematics at Morehouse College, Atlanta, Georgia. He has authored or co-authored around 20 refereed articles in the areas of dynamical systems, differential equations, and numerical analysis. He is an Editorial Board member of Dynamic Systems and Applications and obtained his Ph.D. degree from Georgia Institute of Technology in 1998 before joining Morehouse College that same year.
Dr. M. Sambandham is a Professor of Mathematics at Morehouse College, Atlanta, Georgia. In addition to coauthoring three monographs and publishing 100 refereed research articles, Dr. Sambandham serves as an editor for six international journals. He is the founder and coeditor of Dynamic Systems and Applications and serves on several journal editorial boards. He is a Life Member of the American Mathematical Society and the Marathwada Mathematical Society. Dr. Sambandham received the B.S. degree (1969) from the University of Madras, Chennai, India, the M.Sc. (1971) and Ph.D. (1976) degrees from Annamalai University, Annamalai Nagar, India, and the M.S. degree from the Atlanta University (1986). He was honored as a Fellow of the Indian Society for Probability and Statistics (2024).