Theory and Numerics of PDE (2025) | National Centre for Mathematics

Convener(s)
Name:	Thirupathi Gudi	Satyanarayana Engu
Mailing Address:	Professor Department of Mathematics. Indian Institute of Science Bangalore 560012	Associate Professor Department of Mathematics NIT Warangal- 506004, Telangana Email:
Email:	gudi at iisc.ac.in	satya at nitw.ac.in

PDEs arise naturally in many mathematical modelling describing physical phenomenon and engineering applications. It is therefore important to understand the PDEs and their solution process. The theory of PDEs consists of studying the existence, uniqueness of the solution and further to establish its regularity. The solution process includes to develop methodologies to find solutions either in closed form or by an approximation. The instructional school aims to provide the participants a tour to classical theory of PDEs and to introduce to them the advanced PDEs through Sobolev Spaces. Furthermore, the school aims to demonstrate numeric techniques to solve the PDEs, in particular, finite difference methods and finite element methods. The topics in the school are designed in such way that the participants get exposure to topics in both classical and modern approach in the theory and computation of PDEs which are also part of the curriculum in the universities and post graduate colleges.

Dates:

Monday, September 1, 2025 - 19:00 to Saturday, September 13, 2025 - 19:00

Venue:

Venue Address:

Lecture Hall Complex
NIT Warangal- 506004, Telangana

Venue State:

Telangana

Venue City:

Warangal

PIN:

506004

Syllabus:

Name of the Speaker with affiliation	No. of Lectures	Detailed Syllabus
Satyanarayana Engu Dept. of Mathematics, NIT Warangal Telangana	6	Classical PDE: Laplace equation: Harmonic functions, maximum principle, fundamental solution, Green’s function and the solvability of Dirichlet problem. Heat equation: Weak and strong maximum principles for the heat equation, fundamental solution, existence and uniqueness for the initial value problem.
Manas R Sahoo School of Mathematical sciences, NISER, Bhubaneswar, Odisha	6	Sobolev spaces, definitions, examples, approximation and extension, basic properties, Traces, Sobolev inequalities and compact embedding’s, Poincares inequlities.
Veerappa Gowda G. D., TIFR Centre for Applicable Mathematics, Bengaluru	6	Non-linear hyperbolic conservation laws: Concept of weak solutions, entropy condition and uniqueness of the solution. Construction of Godunov, Lax- Friedrichs, Engquist-Osher and Lax-Wendroff schemes. Lax-Wendroff theorem for convergence of the numerical solution. Finite volume schemes. Monotone schemes: L¹ stability, total variation diminishing property and their convergence to the entropy solution. Higher order schemes. Finite volume schemes in higher dimensions.
Thirupathi Gudi Department of Mathematics, Indian Institute of Science, Bengaluru	6	Finite Element Methods: Construction of finite ele- ment spaces, Polynomial approximation/interpolation theory, FEM for elliptic problems. Finite difference in time and finite elements in space for heat and wave equations. Error analysis.FEM implementation in MATLAB.

References:

L. C. Evans. Partial Differential Equations, AMS.
S. Kesavan. Topics in Functional Analysis and Applications, New Age Int. Publ.
S. Larsson and V. Thomee. Partial differential equations with numerical methods. Springer.
1. R.L. Burden and J.D. Faires, Numerical Analysis, Brooks/Cole, Cengage Learning, 2011
J. W. Thomas, Numerical Partial Differential Equations, Springer Science 1995.
R.J. LeVeque, Numerical Methods for Conservation Laws, Birkhauser, Verlag, 1992
Godlewski E. and P.A. Raviart, Hyperbolic systems of conservation laws, Mathematiques et Applications, ellipses, Paris, 1991.

Time Table:

Day	Date	Lecture 1 (9.30–11.00)	Tea (11.00–11.30)	Lecturer 2 (11.30–1.00)	Lunch (1.00– 2.30)	Tutorial 1 (2.30–3.30)	Tea (3.30- 4.00)	Tutorial 2 (4.00-5.00)	Snacks 5.00-5.30
		(name of the speaker)		(name of the speaker)		(name of the speaker/ tutor)		(name of the speaker/ tutor)
Mon	01/09/ 2025	SN	Tea	MS	Lunch	MS+KD+AG	Tea	SN+AG+KD	Snacks
Tues	02/09/ 2025	SN	Tea	MS	Lunch	MS+KD+AG	Tea	SN+AG+KD	Snacks
Wed	03/09/ 2025	SN	Tea	MS	Lunch	MS+KD+AG	Tea	SN+AG+KD	Snacks
Thu	04/09/ 2025	SN	Tea	MS	Lunch	MS+KD+AG	Tea	SN+AG+KD	Snacks
Fri	05/09/ 2025	SN	Tea	MS	Lunch	MS+KD+AG	Tea	SN+AG+KD	Snacks
Sat	06/09/ 2025	SN	Tea	MS	Lunch	MS+KD+AG	Tea	SN+AG+KD	Snacks
SUNDAY
Mon	08/09/ 2025	VG	Tea	TG	Lunch	VG+AK+SJ	Tea	TG+ SJ +AK	Snacks
Tues	09/09/ 2025	VG	Tea	TG	Lunch	VG+AK+ SJ	Tea	TG+ SJ +AK	Snacks
Wed	10/09/ 2025	VG	Tea	TG	Lunch	VG+AK+ SJ	Tea	TG+ SJ +AK	Snacks
Thu	11/09/ 2025	VG	Tea	TG	Lunch	VG+AK+ SJ	Tea	TG+ SJ +AK	Snacks
Fri	12/09/ 2025	VG	Tea	TG	Lunch	VG+AK+ SJ	Tea	TG+ SJ +AK	Snacks
Sat	13/09/ 2025	VG	Tea	TG	Lunch	VG+AK+ SJ	Tea	TG+ SJ +AK	Snacks

Selected Applicants:

Selected candidates should confirm their participation by replying to the individual email communication sent by the organisers on or before 10th August 2025, failing which the wait listed candidates will be given the opportunity.

Sr.n	SID	Full Name	Gender	Affiliation	Position in College/ University	University/ Institute M.Sc./ M.A.	Year of Passing M.Sc./M.A	Ph.D. Degree Date
1	65436	Dr. Lalit Kumar	Male	Pt. JLN Govt. College Faridabad	Assistant Professor	IIT Bombay, Mumbai	2015	11/25/2024
2	65343	Ms Aishwaraya .	Female	MIT ADT University Pune, Maharastra	Assistant Professor	Malviya national institute of technology Jaipur, India	2017	10/26/2024
3	65388	Dr. Gopal Kumar Gupta	Male	Symbiosis International University Nagpur	Assistant Professor	Banaras Hindu University Varanasi	2011	3/15/2019
4	65345	Dr. Shweta Dubey	Female	Samastipur College, Samastipur	Assistant professor	Mahatma Gandhi Kashi Vidyapith Varanasi	2016	4/25/2025
5	65370	Dr. Pappu Mahto	Male	St. Xavier's College l, Ranchi	Assistant Professor	Ranchi University	2014	07/07/2022
6	65448	Mr. Uzair Ahmed	Male	Jamia Millia Islamia ( A Central University), New Delhi	Asst. Professor	Indian Institute of Technology Kanpur	2020
7	65298	Dr. Gnanasekaran S	Male	National Institute of Technology Tiruchirappalli	Research Associate	University department / Bharathiar University, Coimbatore	2015	08/07/2023
8	65346	Ms Aditi Tomar	Female	IIT Gandhinagar	Postdoctoral fellow	University of Delhi	2017	2/27/2025
9	65456	Dr. Prakash M	Male	KPR Institute of Engineering and Technology, Coimbatore	Assistant Professor III	Department of Mathematics, Bharathiar University.	2010	12/05/2016
10	65461	Dr. Mohd Younus Bhat	Male	Islamic University of Science and Technology Kashmir	Assistant Professor	University of Kashmir	2011	05/04/2017
11	65469	Dr. Raja N	Male	KPR Institute of Engineering and Technology	Assistant Professor III	Bharathiar University	2011	7/22/2019
12	65411	Dr. Gunjan Khurana	Female	I. P. College for Women	Associate Professor	University of Delhi	2007	11/10/2018
13	65297	Mrs. Richa Dhiman	Female	Ram Chandra uniyal government post graduate college Uttarkashi	Assistant Professor	Gurukul Kangri University Haridwar, Uttarakhand	2014
14	65380	Dr. Priya Gupta	Female	Hcpg college	Lecturer	Hcpg college varanasi	2007	02/11/2015
15	65404	Dr Kuparala Venkata Vidyasagar	Male	Government Degree College Bheemunipatnam	Lecturer	ANDHRA UNIVERSITY	2001	6/24/2022
16	65358	Dr. Rajasekar S P	Male	Government Arts College for Women, Nilakottai	Associate Professor	Pondicherry University	2004	9/30/2020
17	65371	Mrs Pichailakshmi Rajesh	Female	SRM TRP ENGINEERING COLLEGE	Assiatant Professor	BHARATHIDASN /SEETHALAKSHMI RAMASWAMI COLLEGE M.Sc MATHS	2005	7/23/2021
18	65508	Dr. Geetan Manchanda	Female	Maitreyi College	Professor		2005	8/27/2021
19	65500	Mrs. Anasuyakumari Maram	Female	National Institute of Technology, Andhra Pradesh	Ph.D. scholar	Andhra University	2022	08/05/2015
20	65363	Mr. Subhrajit Roy	Male	Heramaba Chandra College	Assiatant Professor	Visva-Bharati (A Central University)	2012
21	65367	Mr. Rahul Kar	Male	Kalyani Mahavidyalaya	State Aided Teacher	Burdwan University	2014
22	65425	Ms. Humera Khan	Female	Jamia Millia Islamia	Ph.D. scholar	Chaudhary Charan Singh University, Meerut	2020
23	65541	Mr. Pal Bharatbhai Patel	Male	B. K. M. Science College, Valsad	Adhoc Assistant Professor	Veer Narmad South Gujarat University, Surat	2023
24	65435	Ms Anupama Ghorai	Female	National Institute of Technology, Tiruchirappalli	Ph.D. scholar	Midnapore College (Autonomous)	2019
25	65309	Mr. Himanshu Gangwar	Male	Visvesvaraya National Institute of Technology Nagpur	Ph.D. scholar	National Institute of Technology Hamirpur (H. P.) - 177005, India.	2021
26	65428	Mr. Sachin Kumar Sahu	Male	V.N.I.T., Nagpur	Ph.D. scholar	Sambalpur University M.Sc.	2018
27	65534	Ms. Mahima Sahu	Female	Visvesvaraya National Institute of Technology	Ph.D. scholar	Devi Ahilya Vishwavidyalaya, Indore	2024
28	65398	Mr Mayanglambam Udoy Meitei	Male	Visvesvaraya National Institute of Technology (VNIT)	Junior Research Fellow	CSJM University	2024
29	65393	Ms. Smritikana Pal	Female	NISER Bhubaneswar	Ph.D. scholar	Visva Bharati	2024
30	65384	Mr. Rohit Kumar Mandal	Male	IIT Patna	Ph.D. scholar	IIT Patna	2024
31	65379	Mr. Shivam Sharma	Male	University of Allahabad	Ph.D. scholar	University of Allahabad	2023
32	65311	Ms. Neelam .	Female	NIT Warangal	Ph.D. scholar	NIT Hamirpur	2020
33	65481	Mr. Koshalesh Meher	Male	NIT Warangal	Ph.D. scholar	National Institute of Technology Warangal	2020

School Short Name:

tnpde

Last Date Application:

Sunday, May 28, 2023

School Type:

IST