In an era where engineering challenges are becoming increasingly multifaceted, Mathematical Solutions for Complex Engineering Systems serves as a comprehensive guide bridging the gap between theory and real-world applications. This book explores advanced mathematical modeling techniques, computational approaches, and optimization strategies that drive innovation across various engineering disciplines.
This book brings together a diverse collection of research contributions that highlight:
- Deterministic, stochastic, linear, and nonlinear models essential for analyzing multi-physical systems, from fluid dynamics to reliability engineering.
- Cutting-edge methods such as finite element analysis, boundary element methods, Keller box techniques, and machine learning-driven modeling for solving complex engineering problems.
- Case studies on nuclear power plant reliability, eco-epidemiology, nanofluid heat transfer, and pesticide impact on agricultural sustainability.
- Novel mathematical frameworks, including fractional Taylor wavelets, B-spline methods, and variational principles, for tackling nonlinear differential equations.
- Advanced concepts such as tunnel mathematics, meshfree methods, and high-resolution computational fluid dynamics (CFD) models for solving contemporary engineering challenges.
Designed for researchers, engineers, and graduate students, this book provides a robust foundation in mathematical techniques and their practical applications. With contributions from leading experts, it offers a unique blend of theoretical depth and computational efficiency, making it an essential reference for tackling modern engineering complexities.
Table of Contents:
Chapter 1: Recent Innovations and Advances in Mathematical Modeling for Engineering Systems Chapter 2: A Study of Approximation Techniques used to Solve Queueing Models that Arise in Optimizing Complex Engineering Systems Chapter 3: Stochastic Modeling in Engineering Systems: A study of a Nuclear Power Plant System Chapter 4: Nonlinear Dynamics and Chaos in Engineering Systems: Through an Epidemic Model Chapter 5: Eco-epidemiological Analysis of Plant–Herbivore Interactions: The Allee Effect and Time-dependent Dynamics Chapter 6: Impacts of Pesticides and External Interventions on Crop Production: A Modeling Approach Chapter 7: Tensor Foundations of Tunnel Mathematics Chapter 8: Boundary Element Analysis for MHD Stokes Flow through a Microchannel Exhibiting Surface Roughness Chapter 9: Numerical Investigation of Non-Darcy MHD Boundary Layer Nanofluids Flow Over a Non-linear Stretching Surface Chapter 10 : Extended Hydrodynamic Models for Rayleigh–Brillouin Scattering in Polyatomic Rarefied Gases: A Comparative Study Chapter 11: Nodal Discontinuous Galerkin Framework for Solving Grad-17 Moment Equations in a Rarefied Regime Chapter 12: Exploring the Method of Fundamental Solutions for Nonhomogeneous and Nonlinear Partial Differential Equations Chapter 13: A Fractional order Taylor Wavelets Approach for the Numerical Simulation of Fractional Variational Problems Chapter 14: New Fourth-order Efficient Numerical Solutions of the Klein–Gordon Equation Chapter 15: Numerical Approximation of the Sine–Gordon Equation by Using the Hybrid B-spline Differential Quadrature Method Chapter 16: An Overview of High-resolution Schemes in the OpenFOAM Toolkit
About the Author :
Dr. Satyvir Singh is a Research Associate Fellow at the Institute of Applied and Computational Mathematics, RWTH Aachen University, Germany. He obtained his Ph.D. in Computational Fluid Mechanics from Gyeongsang National University, South Korea, where he developed 3D discontinuous Galerkin methods for solving Boltzmann-type gas kinetic equations. He has held research positions at Nanyang Technological University, Singapore, and the Research Center for Aircraft Parts Technology in South Korea. His expertise spans computational fluid dynamics, high-order numerical methods, gas kinetic theory, and hydrodynamic instability. Dr. Singh has authored over 50 research articles with more than 700 citations and has presented his work globally. He has also received research funding as Co-PI for a project on brain tumor dynamics at Jazan University, Saudi Arabia.
Dr. Mukesh Kumar Awasthi is an Assistant Professor in the Department of Mathematics at Babasaheb Bhimrao Ambedkar University, Lucknow. Specializing in mathematical modeling of flow problems, he has expertise in viscous potential flow, electro-hydrodynamics, magneto-hydrodynamics, and heat and mass transfer. Dr. Awasthi has published over 135 research works, including books and journal articles, and has served as a series editor for CRC Press. He has received multiple research awards and secured funding for his project on nonlinear fluid interfaces. Recognized among the top 2% of researchers worldwide by Stanford University in 2022 and 2023, he continues to contribute significantly to computational mathematics and engineering applications.
