Computational Wave Dynamics explains the analytical, semi-analytical, and numerical methods for finding exact or approximate solutions to various linear and nonlinear differential equations governing wave-like flows. The book explores the latest and most efficient linear and nonlinear differential equations that govern all waves with particular emphasis on water waves, helping the reader to incorporate a more profound numerical understanding of waves in a range of engineering solutions. Procedures, algorithms, and solutions are presented in a simple step-by-step style, helping readers with different backgrounds at various levels to engage with this topic.
Waves exist almost everywhere in nature. Different types include water, sound, electromagnetic, seismic, and shock. The breadth of different methods addressed in this one book creates a uniquely valuable resource for the comparison of equations, and acts as a very useful summary of recent research into computational wave dynamics.
- Tackles ordinary and partial differential equations for wave dynamics, and provides approximation methods for solving them
- Uses easy to understand examples representing wave behavior to help introduce numerical solutions, as well as showing the theoretical justifications for such solutions
- Covers semi-implicit methods, the Kortweg-de-Vries equations, and many others in one resource
- Provides a uniquely valuable resource for the comparison of equations, and acts as a very useful summary of recent research into computational wave dynamics
1. Introduction to water wave equations 2. Recent developments of different methods for solving water wave equations 3. Analytical Methods 4. Semi Analytical Methods 5. Numerical Methods 6. Korteweg-de Vries Equations 7. Shallow Water Equations 8. Burgers' equation 9. Benjamin Bona Mahony equation 10. Equation
Dr. Snehashish Chakraverty has 29 years of experience as a researcher and teacher. Presently he is working in the Department of Mathematics (Applied Mathematics Group), at the National Institute of Technology Rourkela, Odisha, India as a Full Professor. Prior to this he was with CSIR-Central Building Research Institute, Roorkee, India. He has a Ph.D. from IIT Roorkee in Computer Science. Thereafter he did his post-doctoral research at Institute of Sound and Vibration Research (ISVR), University of
Southampton, U.K. and at the Faculty of Engineering and Computer Science, Concordia University, Canada. He was also a visiting professor at Concordia and McGill universities, Canada, and visiting professor at the University of Johannesburg, South Africa. He has authored/co-authored 14 books, published 315 research papers in journals and conferences, and has four more books in development. Dr. Chakraverty is on the Editorial Boards of various International Journals, Book Series and Conferences. Prof. Chakraverty is the Chief Editor of the International Journal of Fuzzy Computation and Modelling (IJFCM), Associate Editor of Computational Methods in Structural Engineering, Frontiers in Built Environment, and is the Guest Editor for several other journals. He was the President of the Section of Mathematical sciences (including Statistics) of the Indian Science Congress. Prof. Chakraverty has undertaken around 16 research projects as Principle Investigator funded by international and national agencies. His present research area includes Differential Equations (Ordinary, Partial and Fractional), Soft Computing and Machine Intelligence (Artificial Neural Network, Fuzzy and Interval Computations), Numerical Analysis, Mathematical Modeling, Uncertainty Modelling, Vibration and Inverse Vibration Problems.
Perumandla Karunakar's research focuses mainly on novel applications of applied mathematics to fluid flow problems. His research has been published in several internationally respected academic journals.