Real-world issues can be translated into the language and concepts of mathematics with the use of mathematical models. Models guided by differential equations with intuitive solutions can be used throughout engineering and the sciences. Almost any changing system may be described by a set of differential equations. They may be found just about anywhere you look in fields including physics, engineering, economics, sociology, biology, business, healthcare, etc. The nature of these equations has been investigated by several mathematicians over the course of hundreds of years and, consequently, numerous effective methods for solving them have been created. It is often impractical to find a purely analytical solution to a system described by a differential equation because either the system itself is too complex or the system being described is too vast. Numerical approaches and computer simulations are especially helpful in such systems.

The content provided in this book involves real-world examples, explores research challenges in numerical treatment, and demonstrates how to create new numerical methods for resolving problems. Theories and practical applications in the sciences and engineering are also discussed. Students of engineering and applied mathematics, as well as researchers and engineers who use computers to solve problems numerically or oversee those who do, will find this book focusing on advance numerical techniques to solve linear and nonlinear differential equations useful.

Dr. Geeta Arora received her Ph.D. degree in Mathematics from IIT Roorkee, India in 2011. She is currently serving as a professor in the department of mathematics at Lovely Professional University, Punjab, India. She has over eleven years of research and teaching experience and has taught several core courses in applied mathematics at undergraduate, postgraduate, and doctorate levels. She has published around 50 research papers in both international and national journals. She has authored eight book chapters in national and international publications. Also, she has written a book on Quick calculations in mathematics and another on statistics. Her area of research is development of numerical methods and statistics. She received the Research Appreciation Award in 2017 and 2019 awarded by Lovely Professional University, Punjab, India. She has conducted several workshops on MATLAB and Vedic mathematics for students and faculty members within and outside the university campus. She has supervised five students and is currently guiding five Ph.D. Scholars.

Professor Mangey Ram received his Ph.D. degree major in mathematics and minor in computer science from G. B. Pant University of Agriculture and Technology, Pant Nagar, India in 2008. He has been a Faculty Member for around thirteen years and has taught several core courses in pure and applied mathematics at undergraduate, postgraduate, and doctorate levels. He is currently the Research Professor at Graphic Era (Deemed to be University), Dehradun, India and Visiting Professor at Peter the Great St. Petersburg Polytechnic University, Saint Petersburg, Russia. Before joining the Graphic Era, he was a Deputy Manager (Probationary Officer) with Syndicate Bank for a short period. He is Editor-in-Chief of International Journal of Mathematical, Engineering and Management Sciences; Journal of Reliability and Statistical Studies; Journal of Graphic Era University; Series Editor of six Book Series with Elsevier, CRC Press, Walter De Gruyter, River Publishers and a guest editor and associate editor for various journals. He has published 300 plus publications (journal articles/books/book chapters/conference articles) in IEEE, Taylor and Francis, Springer Nature, Elsevier, Emerald, World Scientific and many other national and international journals and conferences. Also, he has published more than 60 books (authored/edited) with international publishers like Elsevier, Springer Nature, CRC Press, Walter De Gruyter, and River Publishers. His fields of research are reliability theory and applied mathematics. Dr. Ram is a Senior Member of the IEEE, Senior Life Member of Operational Research Society of India, Society for Reliability Engineering, Quality and Operations Management in India, Indian Society of Industrial and Applied Mathematics, He has been a member of the organizing committee of a number of international and national conferences, seminars, and workshops. He has been conferred with the "Young Scientist Award" by the Uttarakhand State Council for Science and Technology, Dehradun, in 2009. He has also been awarded the "Best Faculty Award" in 2011; "Research Excellence Award" in 2015; "Outstanding Researcher Award" in 2018 for his significant contribution in academics and research at Graphic Era Deemed to be University, Dehradun, India. Recently, he received the "Excellence in Research of the Year-2021 Award" by the Honourable Chief Minister of Uttarakhand State, India, and "Emerging Mathematician of Uttarakhand" state award by the Director, Uttarakhand Higher Education.