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Full 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.
Contents
Elementary Tutorial on Numerical Methods for Singular Perturbation Problems.- Interior Layers in Singularly Perturbed Problems.- Singularly Perturbed Delay Differential Equations and Numerical Methods.- Initial or boundary value problems for systems of singularly perturbed differential equations and their solution profile.- Convergence of the Crank Nicolson Method for a singularly perturbed parabolic reaction-diffusion system.- Iterative Numerical Method for a System of Singularly Perturbed Reaction - Diffusion Equations with Negative shifts.- Parameter Uniform Numerical Method for Second Order Singularly Perturbed Turning Point Problems with Robin Boundary Conditions.- Numerical Method for a Singularly Perturbed Boundary Value Problem for a Linear Parabolic Second Order Delay Differential Equation.- A Parameter Uniform Numerical Method for an Initial Value Problem for a System of Singularly Perturbed Delay Differential Equations with Discontinuous Source terms.- A parameter uniform first order convergent numerical method for a semilinear system of singularly perturbed second order delay differential equations.
