Methods of Mathematical Modeling: Advances and Applications delves into recent progress in this field, highlighting innovative methods and their uses in different domains. This book covers convergence analysis involving nonlinear integral equations and boundary value problems, Navier-Stokes equations in Sobolev-Gevrey spaces, magneto-hydrodynamics of ternary nanofluids with heat transfer effects, vortex nerve complexes in video frame shape approximation, hybrid schemes for computing hyperbolic conservation laws, and solutions to new fractional differential equations. Additionally, the book examines dynamics of Leslie-Gower type predator-prey models and models for the dynamics of generic crop and water availability.
Readers will find diverse approaches, techniques, and applications needed for modeling various physical and natural systems. Each chapter is self-contained, encouraging independent study and application of the modeling examples to individual research projects. This book serves as a valuable resource for researchers, students, educators, scientists, and practitioners involved in different aspects of modeling.
1. Introduction to Mathematical Modeling in Bioscience
2. Construction of Derivative-Free Iterative Schemes with Second and Third
Order from Two Known Data at One Point
3. The Generalized Navier-Stokes Equations with Critical Fractional
Dissipation in Sobolev-Gevrey Spaces
4. Study on Flow of Ternary Nanofluids with Heat Transfer Optimization using
Taguchi Method
5. Hybrid High-Resolution Technique for Numerically Computing Hyperbolic
Conservation Laws
6. Existence of Positive Solutions to a Type of Fractional Differential
Equation
7. Influence of the Allee Effect on Prey in a Modified Leslie-Gower Type
Predation Model Considering Generalist Predators
8. An Efficient Integral Equation Approach to Study Wave Interaction by a
Bottom-Mounted Rectangular Barrier in Presence of a Pair of Partially
Immersed Thin Vertical Barriers
9. Analytic and Computational Treatment of Random Differential Equations via
the Liouville Partial Differential Equation
Dr. Hemen Dutta PhD is a Professor at Gauhati University, India. He also served three other higher learning academic institutions in different capacities prior to joining the Gauhati University. His current research interests are in the areas of nonlinear analysis and mathematical modeling. He is a regular and guest editor of several international indexed journals. He has published 25 books, including Mathematical Modelling and Analysis of Infectious Diseases, New Trends in Applied Analysis and Computational Mathematics, Current Trends in Mathematical Analysis and Its Interdisciplinary Applications from Springer, Concise Introduction to Basic Real Analysis, Topics in Contemporary Mathematical Analysis and Applications, and Mathematical Methods in Engineering and Applied Sciences from CRC Press, and Fractional Order Analysis: Theory, Methods and Applications from Wiley, among others. Dr. Dutta is also an honorary research affiliate and speaker for several international and national events.
