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

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