Differential Equations and Numerical Analysis: Tiruchirappalli, India, January 2015

Description

This book offers an ideal introduction to singular perturbation problems, and a valuable guide for researchers in the field of differential equations. It also includes chapters on new contributions to both fields: differential equations and singular perturbation problems. Written by experts who are active researchers in the related fields, the book serves as a comprehensive source of information on the underlying ideas in the construction of numerical methods to address different classes of problems with solutions of different behaviors, which will ultimately help researchers to design and assess numerical methods for solving new problems. All the chapters presented in the volume are complemented by illustrations in the form of tables and graphs Front Matter....Pages i-xi Front Matter....Pages 1-1 Elementary Tutorial on Numerical Methods for Singular Perturbation Problems....Pages 3-24 Interior Layers in Singularly Perturbed Problems....Pages 25-40 Singularly Perturbed Delay Differential Equations and Numerical Methods....Pages 41-62 Initial or Boundary Value Problems for Systems of Singularly Perturbed Differential Equations and Their Solution Profile....Pages 63-73 Front Matter....Pages 75-75 Convergence of the Crank-Nicolson Method for a Singularly Perturbed Parabolic Reaction-Diffusion System....Pages 77-97 A Numerical Method for a System of Singularly Perturbed Differential Equations of Reaction-Diffusion Type with Negative Shift....Pages 99-116 Numerical Method for a Singularly Perturbed Boundary Value Problem for a Linear Parabolic Second Order Delay Differential Equation....Pages 117-133 A Parameter Uniform Numerical Method for an Initial Value Problem for a System of Singularly Perturbed Delay Differential Equations with Discontinuous Source Terms....Pages 135-150 A Parameter-Uniform First Order Convergent Numerical Method for a Semi-linear System of Singularly Perturbed Second Order Delay Differential Equations....Pages 151-165