دانلود کتاب Differential Equations and Applications: ICABS 2019, Tiruchirappalli, India, November 19–21

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Preface
Contents
Editors and Contributors
Virtual Element Method for Singularly Perturbed Reaction-Diffusion Problems on Polygonal Domains
1 Introduction
2 Virtual Element Method Discretization
3 Asymptotic Behaviour of the Solution
4 Shishkin Meshes for Polygonal Domains
5 Numerical Experiments of VEM on Shishkin Meshes
6 Two-Step Methodology
6.1 The Link-Cutting Condition
6.2 Post-processing the Solution
6.3 Numerical Experiments
References
Global Uniform Convergence of a Numerical Method for a Weakly Coupled System of Singularly Perturbed Convection-Diffusion Equations
1 Introduction
2 Properties of the Exact Solution
3 Discrete Problem
4 Error Analysis
5 Numerical Results
6 Conclusion
References
A Parameter-Uniform Fitted Mesh Method for a Weakly Coupled System of Three Partially Singularly Perturbed Convection–Diffusion Equations
1 Introduction
2 Analytical Results
2.1 Shishkin Decomposition of the Solution
2.2 Estimates for the Bounds of the Derivatives of the Singular Component
2.3 Improved Estimates for the Bounds of the Singular Components
3 Numerical Method
4 Error Analysis
4.1 Error Estimate
5 Numerical Illustrations
References
Numerical Method for a Boundary Value Problem for a Linear System of Partially Singularly Perturbed Parabolic Delay Differential Equations of Reaction-Diffusion Type
1 Introduction
2 The Continuous Problem
3 Analytical Results
4 Improved Estimates
5 The Shishkin Mesh
6 The Discrete Problem
7 Error Estimate
8 Numerical Illustration
9 Conclusion
References
A First-Order Convergent Parameter-Uniform Numerical Method for a Singularly Perturbed Second-Order Delay-Differential Equation of Reaction–Diffusion Type with a Discontinuous Source Term
1 Introduction
2 Analytical Results
3 Improved Estimates
4 The Shishkin Mesh
4.1 The Shishkin Mesh for Case (i)
4.2 The Shishkin Mesh for Case (ii)
5 The Discrete Problem
6 Error Estimate
7 Numerical Illustrations
References
Fitted Numerical Method with Linear Interpolation for Third-Order Singularly Perturbed Delay Problems
1 Introduction
2 Continuous Problem
3 Existence and Stability Results
4 Derivative Estimates
5 Discrete Problem
5.1 Shishkin Mesh
5.2 Finite Difference Scheme
5.3 Discrete Stability Result
6 Error Estimates
7 Nonlinear Problem
8 Numerical Illustration
9 Conclusions
References
A Parameter-Uniform Essentially First-Order Convergence of a Fitted Mesh Method for a Class of Parabolic Singularly Perturbed System of Robin Problems
1 Introduction
2 Solution to the Continuous Problem
3 Analytical Results
4 The Shishkin Mesh
5 The Discrete Problem
6 The Local Truncation Error
7 Error Estimate
8 Numerical Illustration
References
Finite Difference Methods with Interpolation for First-Order Hyperbolic Delay Differential Equations
1 Introduction
2 Problem Statements
2.1 Problem I
2.2 Problem II
3 Finite Difference Methods
3.1 Mesh Points
3.2 Finite Difference Scheme with Piecewise Linear Interpolation for the Problem I
3.3 Finite Difference Scheme with Piecewise Linear Interpolation for the Problem II
3.4 Consistency of the Schemes
3.5 Matrix Method for Stability of the Schemes
4 Error Analysis
5 Numerical Examples
6 Concluding Remarks
References
Fitted Mesh Methods for a Class of Weakly Coupled System of Singularly Perturbed Convection–Diffusion Equations
1 Introduction
2 Analytical Results
2.1 Shishkin Decomposition of the Solution
3 Numerical Method
3.1 Shishkin Mesh
3.2 Discrete Problem
4 Numerical Results
4.1 Error Estimate
5 Numerical Illustrations
6 Conclusions
References
Numerical Analysis of a Finite Difference Method for a Linear System of Singularly Perturbed Parabolic Delay Differential Reaction-Diffusion Equations with Discontinuous Source Terms
1 Introduction
2 The Continuous Problem
3 Analytical Results
4 Improved Estimates
5 The Shishkin Mesh
6 The Discrete Problem
7 Error Estimate
8 Numerical Illustration
9 Conclusion
References