Valarmathi Sigamani & John J. H. Miller 
Differential Equations and Applications 
ICABS 2019, Tiruchirappalli, India, November 19–21

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.

Table of Content

1. Virtual Element Method for Singularly Perturbed Reaction-Diffusion Problems on Polygonal Domains: J.L. Gracia and D. Irisarri.- 2. Global Uniform Convergence for Weakly Coupled System of Singularly Perturbed Convection Diffusion Problems: S. Chandra Sekhara Rao, Varsha Srivastava, and Abhay Kumar Chaturvedi.- 3. A Parameter Uniform Fitted Mesh Method for a Weakly Coupled System of Three Partially Singularly Perturbed Convection-Diffusion Equations: Valarmathi Sigamani, Saravana Sankar Kalaiselvan,  John J H Miller.- 4. Numerical Method for a Boundary Value Problem for a Linear System of Partially Singularly Perturbed Parabolic Delay Differential Equations of Reaction-Diffusion Type: Parthiban Saminathan and Franklin Victor.- 5. 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: Manikandan Mariappan,  John J H Miller,  Valarmathi Sigamani.- 6. Fitted Numerical Method with Linear Interpolation for Third-Order Singularly Perturbed Delay Problems: R. Mahendran and V. Subburayan.- 7. A Parameter Uniform Essentially First-Order Convergence of a Fitted Mesh Method for a Class of Parabolic Singularly Perturbed Robin Problem for a System of Reaction-Diffusion Equations: R. Ishwariya, Valarmathi Sigamani,  John J H Miller.- 8. Finite Difference Method and Analysis for First-Order Hyperbolic Delay Differential Equations: S. Karthick and V. Subburayan.- 9. Fitted Mesh Methods for a Class of Weakly Coupled System of Singularly Perturbed Convection-Diffusion Equations: Saravana Sankar Kalaiselvan, Valarmathi Sigamani,  John J H Miller.- 10. Numerical Analysis of a Finite Difference Method for a Linear System of Singularly Perturbed Parabolic Delay Differential Reaction-Diffusion Equations with Discontinuous Source Terms: Parthiban Saminathan and Franklin Victor. 

  

 

 

 

 

 

 

About the author

Valarmathi Sigamani got her Ph D for her findings on numerical analysis of singular prturbation problems for third order ordinary differential equations. She had been working in Bishop Heber College, Tiruchirappalli for about 34 years and was the Head of the Department of Mathematics for fourteen years and retired as the Vice-Principal of the College.  She is an active researcher in the field of numerical analysis for singular perturbation problems for the past 23 years. She has guided eight students for their Ph D and published many papers in reputed international journals. She has been refereeing for few SCI journals and doing joint research works with the great scientist Prof.John J.H. Miller, Professor, Institute for Numerical Computation and Analysis (INCA) Dublin, Ireland, for the past 16 years. She has edited books and participated in many BAIL (Boundary And Interior Layers) Conferences held once in two years at different places round the globe. She loves teaching.
John J.H. Miller was graduated with a double moderatorship in Mathematics and Natural Sciences from Trinity College, Dublin having first studied modern languages and literature. Obtained a Ph.D. in numerical analysis at the Massachusetts Institute of Technology under the supervision of Professor Gilbert Strang. Now he is a Professor at Institute for Numerical Computation and Analysis (INCA) A96 N8K1.Dublin, Ireland.
Prof. John Miller is a pioneer in the area of constructing robust computational techniques to solve singular perturbation problems arising from the study of Navier-Stokes Equations. He worked on the Fitted Operator Methods and Fitted Mesh Methods for certain classes of singular perturbation problems and the analysis of the convergence of these methods which are among the most cited and used works in the literature. 
Research Gate says that Prof. John Miller’s score in Research Gate is higher than 92.5% of all Research Gate members’ scores.
Shivaranjani Nagarajan is an Assistant Professor in the Department of Mathematics at the National Institute of Technology, Tiruchirappalli, Tamil Nadu. She did her doctoral studies on constructing numerical methods for singularly perturbed delay differential equations under the guidance of Dr. Valarmathi Sigamani. She secured the First rank in Bharathidasan University, Tamil Nadu in her Master’s Programme. During her Doctoral studies, she received the prestigeous Inspire Fellowship from the Department of Science & Technology, Government of India. This fellowship is meant for the first rank holders to do their Ph D if their research proposals also seem to be good. She has publications in reputed International journals. Her research interests include differential equations arising in mathematical biology and currently she is working on systems of singularly perturbed differential equations characterised by two singular perturbation parameters.  
Parthiban Saminathan is an Assistant Professor of Mathematics at Bishop Heber College, Tiruchirappalli, Tamil Nadu. He completed his doctoral studies in numerical analysis of systems of parabolic delay differential equations under the guidance of Dr.V. Franklin, Assistant Professor, Department of Mathematics, Bishop Heber College. He is skilled in Data Science and handling data with ‘R’.  He is very much interested in developing codes animating simple mathematical concepts.