Mathematical Methods in Engineering and Applied Sciences (Mathematics and its Applications)

✍ Scribed by Hemen Dutta (editor)

• Publisher: CRC Press
• Year: 2020
• Tongue: English
• Leaves: 309
• Series: Mathematics and its Applications
• Edition: 1
• Category: Library

✦ Synopsis

This book covers tools and techniques used for developing mathematical methods and modelling related to real-life situations. It brings forward significant aspects of mathematical research by using different mathematical methods such as analytical, computational, and numerical with relevance or applications in engineering and applied sciences.

• Presents theory, methods, and applications in a balanced manner
• Includes the basic developments with full details
• Contains the most recent advances and offers enough references for further study
• Written in a self-contained style and provides proof of necessary results
• Offers research problems to help early career researchers prepare research proposals

Mathematical Methods in Engineering and Applied Sciences makes available for the audience, several relevant topics in one place necessary for crucial understanding of research problems of an applied nature. This should attract the attention of general readers, mathematicians, and engineers interested in new tools and techniques required for developing more accurate mathematical methods and modelling corresponding to real-life situations.

✦ Table of Contents

Cover
Half Title
Series Page
Title Page
Copyright Page
Contents
Preface
Editor
Contributors
Chapter 1 Semi-Analytical Source (SAS) Method for Heat Conduction Problems with Moving Heat Source
1.1 Introduction
1.2 Problem Statement
1.2.1 Dimensionless Problem Statement
1.2.2 Heating Regime of Interest
1.3 SAS Method
1.3.1 Discretization into Sub-intervals
1.3.2 Green’s Function
1.3.3 Construction of Source Terms
1.3.4 Time-Stepping Solution
1.4 Results and Discussions
1.5 Concluding Remarks
Acknowledgment
References
Chapter 2 Complete Synchronization of a Time-Fractional Reaction–Diffusion System with Lorenz Nonlinearities
2.1 Introduction
2.2 The Standard and Fractional Lorenz Systems
2.3 Dynamics of the Fractional Lorenz Model
2.4 Time-Fractional Spatio-temporal System
2.5 Complete Synchronization
2.6 Numerical Results
2.7 Concluding Remarks
References
Chapter 3 Oblique Scattering by Thin Vertical Barriers in Water of Finite Depth
3.1 Introduction
3.2 Mathematical Formulation of the Problem
3.3 Method of Solution
3.4 Upper and Lower Bounds for C
3.5 Partially Immersed Vertical Barrier
3.5.1 Numerical Results
3.6 Submerged Barrier Extending Down to the Bottom
3.6.1 Numerical Results
3.7 Conclusion
3.8 Discussion
Acknowledgments
References
Chapter 4 Existence of Periodic Solutions for First-Order Difference Equations Subjected to Allee Effects
4.1 Introduction
4.2 Basic Concepts
4.3 Main Results
4.4 Application to Renewable Resource Dynamics
4.5 Application to Michaelis–Menten Model
References
Chapter 5 Numerical Investigation of Heat Flow and Fluid Flow in a Solar Water Heater with an Evacuated-Tube Collector
5.1 Introduction
5.1.1 Solar Water Heater
5.2 Mathematical Modeling
5.2.1 Continuity Equation
5.2.2 Navier–Stokes Equation
5.2.3 Energy Equation
5.2.4 Buoyancy-Driven Convection
5.3 Numerical Method
5.3.1 The Finite Volume Method
5.3.2 Convective Heat Flow Computation in a Solar Water Heater
5.4 Problem Description
5.4.1 Heat Flow in a Circular Tube with a Hemispherical Cup at the Bottom of an Evacuated-Tube Solar Collector
5.4.1.1 Governing Equations
5.4.1.2 Initial and Boundary Conditions
5.4.1.3 Results and Discussion
5.4.2 Sensitivity of Various Parameters of the Tube and Initial and Boundary Conditions of Heat Transfer Process
5.4.2.1 Calculation of Heat Transfer Coefficient
5.4.2.2 Calculation of Natural Circulation Flow Rate
5.4.2.3 Results and Discussion
5.4.3 Numerical Simulation of Heat Flow of a Solar Water Heater with an Evacuated-Tube Solar Collector—Two-Dimensional Model
5.4.3.1 Governing Equations
5.4.3.2 Initial and Boundary Conditions
5.4.3.3 Results and Discussion
5.5 Conclusion
List of Symbols
References
Chapter 6 Point Potential in Wave Scattering
6.1 Introduction
6.2 Derivation of the Scattering Equation
6.3 Derivation of the Point Potential
6.4 The Significance of V[sub(ps)]
6.5 The Solution
6.5.1 Special Case: A Dirichlet Sphere
6.6 Generalizations
6.6.1 Displaced Origin, Unbounded Medium
6.6.2 Displaced Scatterer in Confinement
6.6.3 Special Cases
6.7 Formal Theory
6.8 Change of Coordinates
6.9 Suggested Applications
Acknowledgment
References
Chapter 7 Complete Synchronization of Hybrid Spatio-temporal Chaotic Systems
7.1 Introduction
7.2 Preliminaries of Fractional Calculus
7.3 General Synchronization Method
7.4 Case Studies
7.4.1 The Newton–Leipnik Spatio-temporal Chaotic System
7.4.2 The Chua Spatio-temporal Chaotic System
7.4.3 The Lorenz Spatio-temporal Chaotic System
7.5 Summary
References
Chapter 8 Statistical and Exact Analysis of MHD Flow Due to Hybrid Nanoparticles Suspended in C[sub(2)]H[sub(6)]O[sub(2)]-H[sub(2)]O Hybrid Base Fluid
8.1 Introduction
8.2 Mathematical Formulation of the Problem
8.3 Results and Discussion
8.3.1 Parametric Analysis
8.3.1.1 Dimensionless Velocity Field f(h)
8.3.1.2 Dimensionless Temperature Field q(h)
8.3.1.3 Dimensionless Nusselt Number and Skin Friction Coefficient (Nu and Sf)
8.3.2 Statistical Analysis
8.3.2.1 Correlation and Probable Error
8.3.3 Regression Analysis
8.4 Concluding Remarks
Acknowledgments
Appendix
References
Chapter 9 Lyapunov Functionals and Stochastic Stability Analyses for Highly Random Nonlinear Functional Epidemic Dynamical Systems with Multiple Distributed Delays
9.1 Introduction
9.1.1 Random and Non-random Dynamical Systems
9.1.1.1 Stochastic and Deterministic Stability
9.1.1.2 Delays and Nonlinearity in Epidemic Models
9.1.2 Stochastic Differential Equation Epidemic Models
9.2 Formulation of the Epidemic Control Research Problem
9.2.1 Assumptions for the SEIRS Epidemic Model
9.3 Derivation of the Vector and Human Population Dynamics
9.3.1 Vector Dynamics in the SEIRS Epidemic Model
9.3.2 Human Population Dynamics in the SEIRS Epidemic Model
9.3.2.1 Dynamics of the Disease in the Exposed Class
9.3.2.2 Dynamics of Disease in the Removed Population
9.3.2.3 Dynamics of Disease in the Susceptible and Infectious Populations
9.3.3 Combining the Dynamics of SEIRS Epidemic in Vector-Human Populations
9.4 Existence of Positive Solution
9.5 The Equilibria and Types of Stochastic Stabilities
9.6 Stability in Probability
9.6.1 Sensitivity of Stochastic Stability Results to the Delays in the System
9.6.2 Discussion on the Stochastic Stability in Probability Results
9.6.2.1 Effect of the Source of Noise on Stochastic Stability
9.6.3 The Inflated Basic Reproduction Number of the Disease Dynamics
9.6.3.1 Combined Effects of Noise and Delays on Stochastic Stability
9.7 Remarks on Almost Sure and p[sup(th)] Moment Exponential Stabilities
9.8 Conclusion
References
Chapter 10 Linear Multistep Method with Application to Chaotic Processes
10.1 Introduction
10.2 Derivation of Half-Step Method
10.3 Analysis of the Method
10.3.1 Truncation Error and Error Constant
10.3.2 Symmetry of the Integration Scheme
10.3.3 Convergence
10.3.4 Zero Stability of Block
10.4 Numerical Applications of the Method to Chaotic Processes
10.5 Conclusion
References
Index