Differential Equation Based Solutions for Emerging Real-Time Problems

Cover
Half Title
Series Page
Title Page
Copyright Page
Table of Contents
Preface
Editors
Contributors
Chapter 1 Introduction
Chapter 2 Application of Differential Equation in a Flexible Production of Deteriorating Item under Trade Credit Policy
	2.1 Introduction
	2.2 Previous Studies and Literature Gap
		2.2.1 Demand Variability
		2.2.2 Controllable Production Rate
		2.2.3 Deterioration under Trade Credit Scenario
	2.3 Description of Problem, Symbols, and Assumptions
		2.3.1 Problem Definition
		2.3.2 Notation
		2.3.3 Assumptions
	2.4 Mathematical Model
		2.4.1 Holding Cost (HC)
		2.4.2 Ordering Cost (OC)
		2.4.3 Deteriorating Cost (DC)
		2.4.4 Unit Production Cost (UPC)
		2.4.5 Payable Interest (PI)
		2.4.6 Earned Interest (EI)
		2.4.7 Sales Revenue (SR)
	2.5 Solution Methodology
		2.5.1 Necessary Condition
	2.6 Numerical Analysis
		2.6.1 Numerical Comparison with Existing Literature
	2.7 Sensitivity Analysis
	2.8 Managerial Implication
	2.9 Conclusions
	References
Chapter 3 Explosion in a Spherical Cavity Expanding with Decelerated Velocity
	3.1 Introduction
	3.2 Formulation and Constitutive Equations
	3.3 Numerical Computations, Results, and Discussions
		3.3.1 Case I
		3.3.2 Case II
		3.3.3 Case III
		3.3.4 Case IV
	3.4 Remarks and Conclusion
	References
Chapter 4 Importance of Differential Equations in a Retailing Strategy under Credit Period Consideration
	4.1 Introduction
	4.2 Literature Review
		4.2.1 Stock and Price Dependent Demand
		4.2.2 Inventory Model with Trade-Credit
		4.2.3 Model for Deteriorating Products
	4.3 Description of Problem, Symbols, and Assumptions
		4.3.1 Problem Definition
		4.3.2 Symbols
		4.3.3 Assumptions
	4.4 Model Formulation
		4.4.1 Case 1
		4.4.2 Case 2
		4.4.3 Case 1
	4.5 Solution Methodology
	4.6 Numerical Examples
		4.6.1 Comparison with Existing Literature
	4.7 Sensitivity Analysis
	4.8 Managerial Insights
	4.9 Conclusions
	References
Chapter 5 Existence Results for the Positive Solutions of a Third-Order Boundary Value Problem & Numerical Algorithm Based on Bernoulli Polynomials
	5.1 Introduction
	5.2 Preliminaries
	5.3 Existence of Solutions
	5.4 Numerical Methods Based on Bernoulli Polynomials
	5.5 Numerical Results
	5.6 Conclusion
	5.7 Acknowledgements
	References
Chapter 6 An Interred, Inclined Long Strike-Slip Fault in a Striped Elastic/Viscoelastic Medium
	6.1 Introduction
	6.2 Formulation
		6.2.1 Constitutive Equations
			6.2.1.1 Stress-Strain Relations
			6.2.1.2 Equation of Motion for Stress
		6.2.2 Boundary Conditions
		6.2.3 Primodial Conditions
		6.2.4 Conditions in the Range |y2|→∞
	6.3 Components of Forces in the Absence of Fault Movement
	6.4 Components of Forces in Aseismic Period Followed by Sudden Movement Across the Fault
	6.5 Numerical Results and Discussion
		6.5.1 Change of Shear Stress T′[sub(12)] (Due to Fault Slip) with Deep in the Second Layer of the Medium
		6.5.2 Shear Stress T′[sub(12)] with Different Widths of the Fault
	Appendix
	References
Chapter 7 Combined Study on Time-Dependent Deterioration and Carbon Emission for Fixed Lifetime Substitutable/Complementary Product in a Sustainable Supply Chain Management
	7.1 Introduction
	7.2 Literature Review
	7.3 Problem Definition, Notation, and Assumptions
		7.3.1 Problem Definition
		7.3.2 Notation
		7.3.3 Assumptions
	7.4 Mathematical Expression of the Model
		7.4.1 Mathematical Model for Retailer
			7.4.1.1 Ordering Cost
			7.4.1.2 Holding Cost
			7.4.1.3 Deterioration Cost
			7.4.1.4 Disposal Cost
			7.4.1.5 Revenue
		7.4.2 Mathematical Model for Manufacturer-I
			7.4.2.1 Setup Cost
			7.4.2.2 Manufacturing Cost
			7.4.2.3 Holding Cost
			7.4.2.4 Transportation Cost
			7.4.2.5 Revenue
		7.4.3 Mathematical Model for Manufacturer-II
			7.4.3.1 Setup Cost
			7.4.3.2 Manufacturing Cost
			7.4.3.3 Holding Cost
			7.4.3.4 Transportation Cost
			7.4.3.5 Revenue
	7.5 Solution Methodology
	7.6 Numerical Example
		7.6.1 Discussion of the Numerical Example
	7.7 Sensitivity Analysis
	7.8 Managerial Insight
	7.9 Conclusions
	Appendix A
	Appendix B: First and Second-order Derivative
	Appendix C: Hessian Matrix
	References
	Notes
Chapter 8 Framing the Slip Flow of TiO[sub(2)] Nanofluid Past an Inclined Porous Plate Coexistence of Solar Radiation: An Application of Differential Equation
	8.1 Introduction
	8.2 Formulation of Mathematical Model
		8.2.1 Flow Analysis
		8.2.2 Thermophysical Properties of the Nanofluids
		8.2.3 Boundary Conditions
		8.2.4 Transformed Equations
		8.2.5 Parameters of Engineering Significance
	8.3 Numerical Procedure
		8.3.1 Method of Solution
		8.3.2 Code Verification
	8.4 Results and Discussions
		8.4.1 Influence of Velocity Slip Parameter (ξ)
		8.4.2 Influence of Thermal Slip Parameter (ζ)
		8.4.3 Influence of Porosity Parameter (Da)
		8.4.4 Influence of Inertial Parameter (F[sub(s)])
		8.4.5 Influence of Radiation Parameter (R)
	8.5 Conclusions
	References
Chapter 9 Advection-Diffusion Equations and Its Applications in Sciences and Engineering
	9.1 Introduction
		9.1.1 Literature Review
	9.2 Classification
		9.2.1 1D ADE
			9.2.1.1 Initial Condition
			9.2.1.2 Boundary Conditions
		9.2.2 2D ADE
		9.2.3 2D Unsteady ADE
		9.2.4 3D ADE
			9.2.4.1 Initial Condition
			9.2.4.2 Boundary Conditions
		9.2.5 Fractional ADE
	9.3 Applications
		9.3.1 Applications of ADE: In Field of Sciences
		9.3.2 Solutions of ADE: An Analytical Approach
			9.3.2.1 Development of Recurrence Relation for the Solution of 1D ADE by HPM
			9.3.2.2 Development of Recurrence Relation for Solution of 2DADE by HPM
	9.4 Application of ADE: A Numerical Aspect
	9.5 Numerical Methods Developed for Solution of ADE
		9.5.1 Quartic B-spline
		9.5.2 Quintic B-Spline
	9.6 Conclusion
	References
Chapter 10 Differential Equation-Based Analytical Modeling of the Characteristics Parameters of the Junctionless MOSFET-Based Label-Free Biosensors
	10.1 Introduction
	10.2 Model Formulation of the Device
		10.2.1 Boundary Conditions
		10.2.2 Operating Modes
			10.2.2.1 Full Depleted (FD) Mode
			10.2.2.2 Partially Depleted (PD) Mode
			10.2.2.3 Next to Flat-Band (FB) Mode
	10.3 Modeling of the Surface Potential
		10.3.1 Gate Metal M1 (FD Mode) and Gate Metal M2 (PD Mode)
		10.3.2 Gate Metal M1 (PD Mode) and Gate Metal M2 (PD Mode)
		10.3.3 Gate Metal M1 (PD Mode) and Gate Metal M2 (Near FB Mode)
	10.4 Threshold Potential Model
	10.5 Results and Simulations
	10.6 Conclusion
	References
Chapter 11 Application of Differential Equation in Inventory Control
	11.1 Introduction
		11.1.1 The Classical EOQ Model
		11.1.2 EOQ Model Where Demand Is Time-Dependent i.e., D = D (t)
		11.1.3 EOQ Model Where Demand Is Depending upon Stock i.e., D = D(I)
	11.2 Mathematical Model
		11.2.1 Formulation of Mathematical Model Beginning with No Shortage
			11.2.1.1 Case I
			11.2.1.2 Case II
			11.2.1.3 The Policy for Optimal Replenishment
		11.2.2 Formulation of Mathematical Model Starting with Shortages
			11.2.2.1 Case I
			11.2.2.2 Case II
			11.2.2.3 The Optimal Replenishment Policy
	11.3 Numerical Examples
	11.4 Concluding Remarks
	References
Chapter 12 The Behavior of Interacting Faults under Increasing Tectonic Forces
	12.1 Introduction
	12.2 Formulation of Mathematical Model
	12.3 Solution of SSD in Absence of Fault Movement
	12.4 Problem Solution after the Creeping Movement Across F1 for 0 < T ≤ T1 < T2
	12.5 After Commencement of the Fault Creep through Second Fault F2, Result for SSD
	12.6 Numerical Computations
	12.7 Result and Discussion
	12.8 Conclusion
	References
Chapter 13 Applications of Fixed-Point Theory in Differential Equations
	13.1 Introduction
	13.2 Mathematical Model 1
	13.3 Mathematical Model 2
	13.4 Conclusions
	References
Chapter 14 Differential Equation-Based Compact 2-D Modeling of Asymmetric Gate Oxide Heterojunction Tunnel FET
	14.1 Introduction
	14.2 Description of the Device Parameters
	14.3 Model Derivation
		14.3.1 Surface Potential Modeling
		14.3.2 Eigenfunction & Eigenvalue
		14.3.3 Electric Field Modeling
		14.3.4 Drain Current Modeling
	14.4 Results and Discussion
	14.5 Conclusion
	Appendix
	References
Index