Advanced Numerical and Semi-Analytical Methods for Differential Equations is the latest title by authors Snehashish Chakraverty, Nisha Mahato, Perumandla Karunakar, Tharasi Dilleswar Rao.
This student-friendly book deals with various approaches for solving differential equations numerically or semi-analytically depending on the type of equations and offers simple example problems to help readers along. Containing twenty chapters, with each chapter covering different methods and studies that may be used for solving different linear as well as nonlinear ordinary and partial differential equations (ODEs and PDEs), if there is something you are trying to understand, it will be in here.
Generally, engineering problems are governed by different differential equations or system of differential equations. These differential equations may be ODES and PDEs. As such, this book deals with various approaches for solving differential equations numerically or semi-analytically depending on the type of differential equations.
Advanced Numerical and Semi-Analytical Methods for Differential Equations is due to be published in July this year. However, it is now available for preorders on Wiley.com.
If you can’t wait till then to learn more, Fran McMahon took the time to speak with the authors about their book. Read on to hear what they said.
1. Congratulations on the upcoming publication of Advanced Numerical and Semi-Analytical Methods for Differential Equations, which is said to feature both basic and newer numerical methods for those at a graduate level. What led to the decision to target this text at students?
In general every physical system is governed by some type of differential equation. Analytical solution of the differential equation may not exist always. As such, numerical or semi-analytical methods are necessary to handle them. This led to the decision to target this text at students.
2. What were your main objectives during the writing process?
Systematic understanding of the titled methods
Basics of linear and nonlinear differential equations
Traditional as well as recent Semi-Analytical and Numerical Methods
Uncertain differential equations
Step by step problem solving
Student friendly, straight forward and easy understanding of the methods
Solved and unsolved problems
3. This book examines numerical and semi-analytical methods that may be used for solving practical ODEs and PDEs and contains solved example problems. What led to the decision to have the text work like this?
Most of the books that are available in the market discuss either numerical or semi-analytical methods for solving practical ODEs and PDEs. But, the present book includes both the methods in a systematic manner using well known practical examples wherever possible/required.
4. If there is one piece of information or advice that you would want your audience to take away from your book, what would that be?
Handling non-linear differential equations.
5. Who should read the book and why?
This book may be used for teaching advanced methods for solving differential equations to graduates, under graduates and research scholars. This will give a comprehensive knowledge of basic as well as method of solution for linear/nonlinear ODEs and PDEs.
6. Why, do you think, this book of may be of interest now?
The differential equations governing the practical problems may not be solved using analytical technics always. When there is no analytical solution then numerical or semi-analytical methods are advantageous. Most of the books that are available in the market discuss only either numerical or semi-analytical methods for handling linear and nonlinear differential equations. But, the present book presents both the methods in a systematic manner using well known practical examples wherever possible/required.
7. If you were to write a follow up edition, are there any other methods and equations that you would consider exploring?
Yes, we may be interested to write a follow up edition by providing MATLB CODEs for the numerical and semi analytical methods. One more project we may work is that extending the present methods to uncertain form in terms of interval/fuzzy.
8. What is it about the area of numerical and semi-analytic methods that fascinates you?
Differential equations are back bone of every science and engineering problems in general. But, the form of differentia equations depends up on particular application problems. As such we may get ODE or PDE and that to linear or nonlinear. Analytical methods may not possible always to solve these equations. As such this book addresses these challenges to handle the above differential equations using numerical and semi-analytical methods. The above triggers us about the fascination.
9. What other work are you currently working on or has recently been published?
Currently, the authors of the book are working on several different problems like Vibration, Artificial Neural Network problems, static and dynamic problems, shallow/tsunami water wave equations and Radon transport problems. As such, the first author has already published 15 books. Moreover 3 books are on-going with different co-authors.