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Differential equations in engineering : research and applications /

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"This book provides advance research in the field of applications of Differential Equations in engineering and sciences and offers a theoretical sound background along with case studies. It describes the advancement of Differential Equations in real life for engineers. Along with covering many...

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Bibliographic Details
Corporate Author: Taylor & Francis
Other Authors: Goyal, Nupur (Editor), Kulczycki, Piotr (Editor), Ram, Mangey (Editor)
Format: eBook
Language:English
Published: Boca Raton, FL : CRC Press, 2022.
Edition:First edition.
Series:Mathematical engineering, manufacturing, and management sciences
Subjects:
Engineering mathematics.
Differential equations.
Mathématiques de l'ingénieur.
Équations différentielles.
TECHNOLOGY / Operations Research
MATHEMATICS / Differential Equations
Differential equations
Engineering mathematics
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Cover
  • Half Title
  • Series Page
  • Title Page
  • Copyright Page
  • Table of Contents
  • Preface
  • Acknowledgments
  • Editors
  • Contributors
  • Chapter 1 Element-Free Galerkin Method for Computational Fracture Mechanics
  • 1.1 Introduction
  • 1.2 Historical Developments in Meshfree Methods
  • 1.3 Element-Free Galerkin Method
  • 1.4 Moving Least Square (MLS) Approximations
  • 1.5 Efficient Calculation of the Shape Function
  • 1.6 Weight Function
  • 1.7 Numerical Integration
  • 1.8 Domain of Influence
  • 1.9 Imposition of Boundary Conditions
  • 1.10 Governing Equation
  • 1.11 Crack Modeling in the Element-Free Galerkin Method
  • 1.11.1 Extrinsic MLS Enrichment
  • 1.11.2 Intrinsic MLS Enrichment
  • 1.12 Integration Integral
  • 1.13 Applications of Element-Free Galerkin Methods to Computational Fracture Mechanics
  • 1.13.1 Crack Modeling under Mechanical Loads
  • 1.13.2 Modeling of Vertical Bi-Material Interface
  • 1.13.3 Modelling of Bi-Metallic Interfacial Edge Crack
  • 1.13.4 Modeling of Thermoelastic Fracture
  • 1.13.4.1 Centre Crack in Square Domain
  • 1.13.5 Thermal Fracture in Coatings
  • 1.13.5.1 Edge Crack with a Thermal Load
  • 1.14 Conclusion
  • References
  • Chapter 2 Evaporative Capillary Instability of Swirling Fluid Layer with Mass Transfer
  • 2.1 Introduction
  • 2.2 Mathematical Description
  • 2.2.1 Basic State
  • 2.2.2 Perturbed State
  • 2.3 Dimensionless Form of the Dispersion Relationship
  • 2.4 Numerical Results and Discussions
  • 2.5 Conclusions
  • Acknowledgment
  • References
  • Chapter 3 Control Instruments of Regularized Problems Based on Mathematical Modeling of Structural Perturbations with Applications at the Nodes of 25-Bar Truss Systems
  • 3.1 Introduction
  • 3.2 Family of Linear Elastic Partial Differential Equations with Explicit Consideration of Structural Perturbations.
  • 3.2.1 Family of Constrained Ill-Posed Optimal Control Problems Due to Structural Perturbations
  • 3.3 Family of Regularized Ill-Posed Optimal Control Problems with State and Structural Perturbation Constraints
  • 3.4 Applications to Real-world Measurements: Structural Perturbation Models Imposed at the Nodes of 25-Bar Truss Systems and Regularization of the Control Instruments
  • 3.4.1 Interpretations of Results: Control Instruments of the Optimal Mass Design of 25-Bar Truss Systems with Loading Conditions Imposed at the Node Elements
  • 3.5 Discussion
  • 3.6 Conclusion
  • Conflict of Interest
  • Acknowledgments
  • References
  • Chapter 4 Numerical Simulation of Singularly Perturbed Differential Equation with Large Delay Using Exponential B-Spline Collocation Method
  • 4.1 Introduction
  • 4.2 Analysis of Recent Numerical Work Carried out on SPDDE
  • 4.3 Considered Boundary Value Problem
  • 4.4 The Exponential Cubic B-spline Collocation Method
  • 4.5 Convergence Analysis
  • 4.6 Numerical Examples
  • 4.7 Discussion and Conclusions
  • References
  • Chapter 5 Application of Differential Equations to Instability of Nanofluids
  • 5.1 Introduction
  • 5.2 Formulation of the Problem and Conservation Equations
  • 5.3 Solution for Model 1: Initially, Volume Fraction Varies in the Vertical Direction
  • 5.4 Solution for Model 2: Initially, Volume Fraction Remains Constant
  • 5.5 Discussions and Comparative Studies of the Results
  • 5.6 Numerical Results and Discussions
  • 5.7 Conclusions
  • References
  • Chapter 6 Analysis of Prey-Predator Model
  • 6.1 Introduction
  • 6.2 Description of Method
  • 6.2.1 Case 1
  • 6.2.2 Theorem 1
  • 6.2.3 Case 2
  • 6.2.4 Theorem 2
  • 6.2.5 Case 3
  • 6.3 Stability Analysis
  • 6.3.1 Theorem 3
  • 6.4 Stability Analysis for Prey-Predator Model
  • 6.5 Applications
  • 6.5.1 Disease Model
  • 6.5.1.1 Case 1
  • 6.5.1.2 Case 2.
  • 6.5.1.3 Case 3
  • 6.5.2 Numerical Illustration
  • 6.5.2.1 Case 1
  • 6.5.2.2 Case 2
  • 6.5.2.3 Case 3
  • 6.6 Results and Discussion
  • 6.7 Conclusion
  • References
  • Chapter 7 Incremental Harmonic Balance Method for Multi-Degree-of-Freedom System with Time-Delays
  • 7.1 Introduction
  • 7.2 Formulation of IHB Method for Delay Differential Equations
  • 7.3 Path-Following and Parametric Continuation
  • 7.4 Stability Analyses of Periodic Solutions
  • 7.4.1 Floquet's Theory for an Uncontrolled System, Using Hsu's Scheme
  • 7.4.2 Floquet's Theory for a Time-Delay System by the Semi-Discretization Method
  • References
  • Chapter 8 Solution to the Dirac Equation
  • 8.1 Introduction
  • 8.2 Preliminaries
  • 8.3 Solution to the Massless Field
  • 8.4 Solution to the Anti-Massless Field
  • 8.5 Results
  • 8.6 Discussion
  • 8.7 Conclusions
  • 8.8 Acknowledgments
  • References
  • Chapter 9 Periodic Solution of a Nonlinear Economic Cycle Model with a Generic Investment Function
  • 9.1 Introduction
  • 9.2 Economic Cycle Model
  • 9.3 Implicit Harmonic Balance Procedure
  • 9.4 Numerical Analysis
  • 9.4.1 The Comparison of the Periodic Solution with the Simulation Result
  • 9.4.2 The Periodic Solution of the Nonlinear Economic Cycle Model
  • 9.4.3 The Effects of the Quadratic Term on the Periodic Solution
  • 9.5 Conclusions
  • Appendix
  • Trigonometric Identities
  • References
  • Chapter 10 Response Evolution of a Marine Riser in Random Sea Waves
  • 10.1 Introduction
  • 10.2 Marine Riser System
  • 10.3 Path Integration Procedure
  • 10.4 Numerical Analysis
  • 10.4.1 The Case of Slight Geometric Nonlinearity
  • 10.4.2 The Case of Strong Geometric Nonlinearity
  • 10.4.3 The Case of Strong Correlation between Excitations
  • 10.5 Conclusion
  • References
  • Chapter 11 Solution of System of PDE Governed in Natural Convective Flow in a Rectangular Porous Cavity.
  • 11.1 Introduction
  • 11.2 Model Formulation
  • 11.3 Governing Equations
  • 11.4 Non-Dimensional Equations
  • 11.5 Solution Procedure
  • 11.6 Stream Function and Nusselt Number
  • 11.7 Interpretation of Results
  • 11.8 Conclusions
  • References
  • Index.