Advanced Computational and Mathematical Approaches in Applied Differential Equations

Advanced Computational and Mathematical Approaches in Applied Differential Equations explores cutting-edge techniques and methodologies in solving complex differential equations, a cornerstone of mathematical modeling across science and engineering. The book bridges theory and application, offering advanced computational strategies and innovative mathematical insights to address real-world problems. Beginning with an overview that presents a unified framework that defines the types of differential equations covered (e.g. ordinary, partial, fractional, fuzzy), the book then progresses to foundations and methods such as Lie symmetries, homotropy, Adomian, FEM, FDM, spectral, machine learning, fuzzy, and fractional derivatives, addressing both computational and mathematical dimensions. Differential equations are fundamental to modeling complex systems, yet solving them often involves significant challenges due to their complexity and nonlinearity. The book equips readers with advanced tools and methodologies to overcome these challenges, providing innovative solutions that improve accuracy, efficiency, and applicability in real-world scenarios. Ideal for researchers, practitioners, and advanced students, it provides a comprehensive resource for tackling challenging applied differential equations with better precision and efficiency.

Table of Contents:
1. Introduction to Differential Equations in Applied Mathematics (Overview of Types of Differential Equations, Methods, and Applications) Part I. Methods for Solving Differential Equations 2. Computational Methods for Partial Differential Equations 3. Computational PDEs Using Finite Element Method (FEM) 4. Hyperbolic Partial Differential Equations 5. Lie Group and Spectral Analysis in Differential Equations Part II. Applications in Various Fields 6. Peristaltic Propulsion of Jeffrey Nanofluid 7. Fuzzy Structural Analysis Problems 8. MHD-Casson Hybrid Nanofluid Flow Over a Permeable Stretching Sheet 9. Effects of Variable Viscosity and Thermal Conductivity on Forced Convection in Bidisperse Porous Medium 10. Jeffrey Fluid Flow in a Sloping Channel 11. Computational Fluid Dynamics 12. Wave Equation with Fuzzy Parameters 13. Mathematical Model of Flowing Channel/Tube with Permeability and Nonuniformity 14. Heat and Mass Transfer 15. Chaotic Dynamics in the Fractional-Order Chua’s Attractor Model 16. McKendrick–von Foerster Equation with Diffusion 17. Free Vibration Analysis of Functionally Graded Sandwich Plates

About the Author :
Dr. Snehashish Chakraverty is a Senior Professor in the Department of Mathematics (Applied Mathematics Group), National Institute of Technology Rourkela, with over 30 years of teaching and research experience. A gold medalist from the University of Roorkee (now IIT Roorkee), he earned his Ph.D. from IIT Roorkee and completed post-doctoral work at the University of Southampton (UK) and Concordia University (Canada). He has also served as a visiting professor in Canada and South Africa. Dr. Chakraverty has authored/edited 38 books and published over 495 research papers. His research spans differential equations (ordinary, partial, fractional), numerical and computational methods, structural and fluid dynamics, uncertainty modeling, and soft computing techniques. He has guided 27 Ph.D. scholars, with 10 currently under his supervision. He has led 16 funded research projects and hosted international researchers through prestigious fellowships. Recognized in the top 2% of scientists globally (Stanford-Elsevier list, 2020–2024), he has received numerous awards including the CSIR Young Scientist Award, BOYSCAST Fellowship, INSA Bilateral Exchange, and IOP Top Cited Paper Awards. He is Chief Editor of International Journal of Fuzzy Computation and Modelling and serves on several international editorial boards. Dr. Srinivas Suripeddi is a distinguished academician and researcher in Applied Mathematics, currently serving as Professor (Higher Academic Grade) at the Department of Mathematics, School of Advanced Sciences, VIT-AP University, Amaravati. He earned his Ph.D. in Fluid Dynamics from NIT Warangal in 1992 under the guidance of the late Prof. N.Ch. Pattabhi Ramacharyulu. With over three decades of teaching and research experience, Prof. Srinivas has published more than 110 papers in reputed national and international journals. His primary research interests include physiological fluid dynamics, magnetohydrodynamics, nanofluid flows, and heat and mass transfer. Dr. Suripeddi holds two patents and has delivered numerous invited talks and chaired sessions at prestigious conferences. He continues to play a key role in mentoring researchers and contributing to scientific advancements in mathematical modeling and applied sciences. Dr. Karunakar Perumandla is currently serving as an Assistant Professor of Mathematics at VIT-AP University, Amaravathi. He obtained his Ph.D. in Mathematics from the National Institute of Technology, Rourkela, focusing on shallow water wave equations, fuzzy and interval analysis, and numerical methods. He holds an M.Sc. in Mathematics from NIT Warangal and a B.Ed. in Mathematics. With over 12 years of teaching experience, Dr. Karunakar has held academic positions at institutions such as Anurag University, Amrita Vishwa Vidyapeetham, and Annamacharya Institute of Technology and Science. He has also been a visiting faculty member at IIIT Vadodara. Dr. Karunakar has published extensively, including multiple book chapters, and co-authored books such as Wave Dynamics (World Scientific) and Advanced Numerical and Semi Analytical Methods for Differential Equations (Wiley). His research explores fuzzy modeling, fractional differential equations, wave dynamics, and computational fluid mechanics. He received the BRNS-DAE scholarship from the Government of India and the Prathibha Puraskar Award for academic excellence. Dr. Karunakar’s ongoing research contributes to the advancement of mathematical modeling under uncertainty and computational techniques in applied sciences.