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

ISBN-13: 9788132235965 / Angielski / Twarda / 2016 / 165 str.

S. Valarmathi; John J. H. Miller; N. Ramanujam

Opis

This book offers an ideal introduction to singular perturbation problems, and a valuable guide for researchers in the field of differential equations.

Spis treści

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.

O autorze

Valarmathi Sigamani is assistant professor at the Department of Mathematics at Bishop Heber College, Tiruchirappalli, Tamil Nadu, India. She did her doctoral studies in numerical analysis at Bharathidasan University, Tiruchirappalli, under the guidance of Prof. N. Ramanujam. She has been teaching algebra, analysis, topology, calculus of variations, computer programming and differential equations to undergraduate and postgraduate students of mathematics. She has published 20 research articles in various reputed international journals and has guided 5 students and guiding some more in their doctoral studies in singular perturbation problems and numerical analysis. Currently, she is working on the qualitative and quantitative analysis of singularly perturbed multi-scale dynamical systems and their applications in biology. She is a council member of the Institute of Numerical Computation and Analysis (INCA), Dublin, Ireland, and is a member in various mathematical societies.