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

Description

This book collects select papers presented at the International Conference on Applications of Basic Sciences, held at Tiruchirappalli, Tamil Nadu, India, from 19-21 November 2019. The book discusses topics on singular perturbation problems, differential equations, numerical analysis, fuzzy logics, fuzzy differential equations, and mathematical physics, and their interdisciplinary applications in all areas of basic sciences: mathematics, physics, chemistry, and biology. It will be useful to researchers and scientists in all disciplines of basic sciences. This book will be very useful to know the different scientific approaches for a single physical system. 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