IST Differential Equations - Theory, Methods and Applications (2019)

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Venue: Bharathiar University,  Coimbatore, Tamil Nadu
Date:  18th, Nov 2019 to 30th, Nov 2019

 

School Convener(s)

Name Prof. S Saravanan Prof. G D Veerappa Gowda
Mailing Address

Head – Department of Mathematics
Bharathiar University
Coimbatore 641 046

Dean – TIFR Centre for Applicable Mathematics
Sharada Nagar, Chikkabommasandra,
Post bag No.6503,
Bangalore 560 065

 


 Speakers with their affiliations:

Name of the speaker

Affiliation

A Adimurthi Professor, TIFR CAM (AA)
G D V Gowda Professor, TIFR CAM (GDVG)
P Kandaswamy Former Professor, Bharathiar University (PK)
R Sahadevan Former Professor, RIASM (RS)
Y V S SSanyasiraju Professor, IIT Madras (YVSSS), IIT Hyderabad
P G Siddheshwar, Professor, Bangalore University (PGS)
S Sundar Professor, IIT Madras (SS)
Guest Speaker:
M Lakshmanan
Professor – Centre for Nonlinear Dynamics, Bharathidasan University (ML)

 List of Tutors

Name of the tutor

Affiliation

Nilanjan Bag

IIT Guwahati

Pramath Anamby

IISc Bangalore

Manish Kumar Pandey

HRI, Allahabad

 


 Syllabus:

 

Sr.

Speaker

Affiliation

 Detailed Syllabus

1 A Adimurthi Professor, TIFR CAM

Elliptic partial differential equations:Gauss-Green theorem, Integration by parts formula, fundamental solution for Laplace equation, solving Poisson equation in Rn, Harnack’s inequality, Green’s functions, representation formula for the solution of boundary value problem by using Green’s function. Green’s functions for a ball and for an upper half plane.

2 G D V Gowda Professor, TIFR CAM

First order nonlinear equations: First order partial differential equations: Introduction to PDE, solving linear, semilinear, quasilinear  and fully nonlinear first order equations by using the method of characteristics. Examples and their applications in various fields.

3 P Kandaswamy Former Professor, Bharathiar University Applications of IBVPs:ode model - human immune system, system of equations, phase plane analysis and interpretation, two extreme cases. pde models - gravity waves and their occurrence in atmosphere, critical levels and their significance, the energy and momentum transfer; double diffusive convection and its solutions, finger and other instabilities.
4 R Sahadevan Former Professor, RIASM Applications of Lie group to Differential Equations: Lie group, Transformation group, applications of Lie group to nonlinear ODE and nonlinear PDE
5 Y V S SSanyasiraju Professor, IIT Madras Numerics for parabolic and hyperbolic partial differential equations : basic finite difference approximation of parabolic and hyperbolic pde,  truncation  error, convergence  through stability  and consistency, higher order and compact approximations, application to some of the benchmark problems from incompressible flows
6 P G Siddheshwar, Professor, Bangalore University Numerics for ordinary differential equations (IVPs and BVPs):Initial Value problems: Euler's method, Higher order Taylor's method, Runge-Kutta method, stability and convergence. Boundary value problems with or without eigenvalues: shooting method for nonlinear problems, finite difference methods for boundary value problems, etc.
7 S Sundar Professor, IIT Madras Meshfree methods: Boundary value problems: meshfree method, 2D incompressible Navier-Stokes Equations, solution for applications involving Coutte flow, Poiseuelle flow, driven cavity flow, broken dam free surface flow, etc.
8 Guest Speaker:
M Lakshmanan
Professor – Centre for Nonlinear Dynamics, Bharathidasan University Basics of Solitons in Nonlinear Dispersive
Partial Differential Equations

 


 Time Table

Day Date Lecture 1
(9.45–11.15)
  Lecture 2
(11.45–1.15)
  Tutorial 1
(2.30–3.30)
  Tutorial 2
(4.00-5.00)
 
Mon 18 Nov ‘19 PGS T
E
A
PGS L
u
n
c
h
PGS+ SA T
E
A
PGS+SA S
n
a
c
k
s
Tues 19 Nov ‘19 PGS PGS PGS+SA PGS+SA
Wed 20 Nov ‘19 PK PK ML+SA PK+SA
Thu 21 Nov ‘19 AA ML GDVG+SA AA+SA
Fri 22 Nov ‘19 GDVG AA GDVG+SA AA+SA
Sat 23 Nov ‘19 AA GDVG AA+SA GDVG+SA
 Sunday : Off
Mon 25 Nov ‘19 GDVG T
E
A
AA  L
u
n
c
h
GDVG+RK T
E
A
AA+ RK S
n
a
c
k
s
Tue 26 Nov ‘19 PK PK PK+ RK PK+ RK
Wed 27 Nov ‘19 YVSSS YVSSS YVSSS + RK YVSSS + RK
Thu 28 Nov ‘19 YVSSS YVSSS YVSSS + RK YVSSS + RK
Fri 29 Nov ‘19 SS SS SS+ RK SS+ RK
Sat 30 Nov ‘19 RS RS RS+ RK RK
  • A Adimurthi  (AA)

  • G D V Gowda (GDVG)

  • P Kandaswamy (PK)

  • R Sahadevan (RS)

  • Y V S SSanyasiraju (YVSSS)

  • P G Siddheshwar  (PGS)

  • S Sundar  (SS)

  • M Lakshmanan (ML)

  •  S Aiyappan, Post Doc, TIFR CAM (SA)

  •  R Kumar, Post Doc, TIFR CAM (RK)

 


List of actual Participants

Sr SID Full Name Gender Affiliation Position in College / University Univ./ Inst. M.Sc./ M.A. Year of Passing
M.Sc./ M.A
Ph.D.
Deg date
1 30679 Dr. Veeramani C Male PSG College of Technology Asst. Prof. Bharathidasan university 2005 19/05/ 2013
2 30726 Mr S Mahesh Male Kathir College of Engineering Asst. Prof. A.V.V.M Sri Pushpam College (Autonomous) 2011  
3 30729 Dr Maddileti Pasupula Male University College Of Science & Informatics,
Mahatma Gandhi University
Asst. Prof. Osmania University 2006 21/09/ 2011
4 30742 Dr Manisha Chaudhary Female MITS, Gwalior (M.P.) Asst. Prof. M.Sc. 2009 22/12/ 2017
5 30745 Mr. Jeshua Rajan Male St. John's College Asst. Prof. St. John's College, Palayamkottai 2016  
6 30751 Ms Jaya Lakshmi P Female Sri GVG Visalakshi College For Women Asst. Prof. Sri GVG Visalakshi College For Women(Autonomous) 2006  
7 30759 Dr. A. Vadivel Male Government Arts College(Autonomous), Karur-5. Asst. Prof. Periyar University 2003 11/02/ 2011
8 30784 Dr Syed Ali Male Thiruvalluvar Univeristy Asst. Prof. Msc 2005 22/12/ 2010
9 30804 Ms. Soniya Dhama Female Indian Institute of Technology Mandi PhD IIT Delhi / M.Sc 2015  
10 30815 Ms Vaishnavi S Female Vellore Institute Of Technology-Chennai Research Scholar - Phd M.sc. Applied Mathematics in Anna university-MIT campus 2018  
11 30827 Dr. Velmurugan Gandhi Male Sultan Qaboos University Post Doctoral Sri Ramakrishna Mission Vidyalaya College of Arts and Science 2010 26/05/ 2017
12 30855 Mr Karnan A Male The Gandhigram Rural Institute (Deemed to be University) PhD The Gandhigram Rural Institute (Deemed to be University) 2017  
13 30856 Ms. Shafiya M Female The Gandhigram Rural Institute (Deemed to be University) PhD The Gandhigram Rural Institute (Deemed to be University) 2018  
14 30907 Ms Garima Garima Female SOUTH ASIAN UNIVERSITY PhD KURUKSHETRA UNIVERSITY KURUKSHETRA 2016  
15 30915 Mrs Anitha Sakthivel Female Sri ramakrishna engineering college PhD PSGR Krishnammal College for women 2014  
16 30952 Dr. Vidhya Ks Female Kumaraguru College of Liberal Arts and Science Asst. Prof. Sri G.V.G. Visalakshi College for Women, Udumalpet 2004 12/08/ 2016
17 31020 Ms. Loganayaki S Female Sri G.V.G Visalakshi College for Women Asst. Prof. Sri G.V.G Visalakshi College for Women 2017  
18 31032 Ms. Sangeeta Devi Female NIT Kurukshetra PhD Student Kurukshetra University, Kurukshetra 2016  
19 31040 Dr. D Prakash Male SRM University Asst. Prof. Bharathiar University 2009 13/08/ 2014
20 -- Dr.Sathiyaseelan D   Manonmanium Sundaranar University, Tirunelveli. Asst. Prof.      
21 -- Mr. B. Ganesh Kumar   Bharathiar University, Coimbatore Research Scholar      
22  -- Ms. M. Kousalya   Bharathiar University, Coimbatore Research Scholar      
23 -- Mrs. R. Baranitha   Bharathiar University, Coimbatore Research Scholar      
24  -- Ms. L. Ramya   Bharathiar University, Coimbatore Research Scholar      
25 -- Mrs. V. Annapoorani   Bharathiar University, Coimbatore Research Scholar      
26 -- Mr. K, Udhayakumar   Bharathiar University, Coimbatore Research Scholar      
27 -- Mr. P. Nirvin   Bharathiar University, Coimbatore Research Scholar      
28 -- G.Divya   IIT, Tirupati Research Scholar      

 


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