Hi, this is Harvindra Singh, a National Postdoctoral Fellow at IIT Ropar, working with Prof. Manoranjan Mishra . I completed my Ph.D. from IIIT Jabalpur and my M.Sc. from IIT Ropar. My research mainly focuses on solving nonlinear PDEs using polynomial spectral methods. Currently, I am exploring finite difference methods (FDM) and developing hybrid spectral-finite difference schemes for applications in financial mathematics. Beyond research, I enjoy singing and have won several prizes in singing competitions over the years.

Computational Methods for PDEs Scientific Computing Numerical Analysis Spectral Methods Finite Difference Methods Computational Finance
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Dr. Harvindra Singh
Dr. Harvindra Singh
ANRF N-PDF Fellow, IIT Ropar
Research Focus

Research Areas

01
Spectral & Pseudospectral Methods
Legendre and Chebyshev discretization schemes for high-accuracy approximation of time-dependent PDEs.
02
Nonlinear Evolution Equations
Numerical analysis of multidimensional Burgers, Burgers–Fisher, and generalized nonlinear parabolic equations.
03
Filter-Enhanced Collocation
Fast algorithms with spectral filtering for polynomial collocation on non-smooth discontinuous problems.
04
Computational Fluid Dynamics
High-order numerical schemes for quasi-linear fluid dynamics and robust solvers for convection-dominated flows.
05
Computational Finance
Numerical methods for option pricing via Black-Scholes and Heston stochastic volatility models.
Research Output

Journal Publications

2026
Efficient filter-enhanced polynomial collocation method for solving discontinuous and steep gradient problems
Harvindra Singh & Lokendra K. Balyan
International Journal of Computer Mathematics · Taylor & Francis · May 2026
SCI First Author
DOI ↗
2026
An efficient high-order solver for multidimensional nonlinear time-evolution (Burgers) equation based on Legendre pseudospectral method
Harvindra Singh & Lokendra Balyan
Computational and Applied Mathematics · Springer Nature · Vol. 45, Article 338, April 2026
SCI First Author
DOI ↗
2025
Optimized Computational Solver for the Quasi-Linear Burgers Equation Using Legendre Pseudospectral Technique
Harvindra Singh & Lokendra Balyan
International Journal of Applied and Computational Mathematics · Springer Nature · Vol. 11, Article 108, May 2025
Scopus First Author
DOI ↗
2024
A numerically robust and stable time–space pseudospectral approach for multidimensional generalized Burgers–Fisher equation
Harvindra Singh, L.K. Balyan, A.K. Mittal, P. Saini
Mathematics and Computers in Simulation · Elsevier · Vol. 225, pp. 177–194, May 2024
SCI First Author
DOI ↗
2024
Pseudospectral analysis for multidimensional fractional Burgers equation based on Caputo fractional derivative
Harvindra Singh, A.K. Mittal & L.K. Balyan
Arabian Journal of Mathematics · Springer Nature · Vol. 13, pp. 409–424, July 2024
Scopus First Author
DOI ↗
2022
Pseudospectral analysis and approximation of two-dimensional fractional cable equation
Avinash Mittal, Lokendra K. Balyan, Manoj K. Panda, Parnika Shrivastava, Harvindra Singh
Mathematical Methods in the Applied Sciences · Wiley · Vol. 45, No. 14, pp. 8613–8630, Sep 2022
SCI
DOI ↗

Conference Papers & Workshops

2024
An Efficient Pseudospectral Approximation of Non-Linear Time-Evolution Equations
CTAC 2024 — Monash University, Australia, Nov 19–22, 2024
International
Link ↗
2024
Improved Pseudospectral Approximation for Nonlinear Parabolic Equation
ICNACT 2024 — VIT Bhopal in collaboration with UTM Mexico, Aug 8–10, 2024 · Published in De Gruyter, 2025
International
DOI ↗
2023
An Improved Chebyshev Collocation Approximation of the Burgers-Fisher Equation
ICAMM 2023 — IIT Indore, Oct 18–20, 2023 · Springer, Vol. 517, pp. 443–446
International
DOI ↗
2023
Workshop on Finite Volume and Spectral Methods for Hyperbolic Problems
Centre for Applicable Mathematics, TIFR Bangalore, Dec 4–15, 2023
Workshop
Link ↗
2022
Spectral Approximation For Elliptic Eigenvalue Problem On Non-Smooth Domain
ICNAA 2022 — Assam Don Bosco University / UTM Mexico / RJ College Mumbai, Nov 22–23, 2022
International
Link ↗
Academic Background

Education Journey

2019 — 2025
Ph.D. in Applied Mathematics
IIIT Jabalpur, Madhya Pradesh, India ↗
Thesis: Robust high-order numerical techniques for solving time-dependent non-linear smooth and non-smooth PDEs using spectral methods
Supervisor: Dr. Lokendra K. Balyan ↗
Degree Awarded: April 22, 2025
Grade : 9.3
2015 — 2017
M.Sc. in Mathematics
IIT Ropar, Punjab, India ↗
First Division
2011 — 2014
B.Sc. in Mathematics, Physics & Chemistry
KLDAV PG College Roorkee, HNB Garhwal University, Uttarakhand ↗
First Division
2011
Intermediate (Class XII)
NIC Dhanauri, Uttarakhand ↗
First Division
Professional History

Teaching & Research Experience

2025 — Present
Current
ANRF National Post-Doctoral Fellow
Indian Institute of Technology Ropar
Rupnagar, Punjab — 140001, India
Autonomous Institute of National Importance · Awarded by ANRF for 2 years
Oct 2024 — 2025
Assistant Professor, Mathematics
Dev Bhoomi Uttarakhand University
Chakrata Road, Dehradun — 248007, Uttarakhand
School of Allied Sciences · Private, UGC-recognized University
Jul 2018 — Aug 2019
Assistant Professor, Mathematics
Chandigarh University
NH-95, Gharuan, Mohali, Punjab — 140413
Private, UGC-recognized University
2019 — 2025
Teaching Assistant (Ph.D.)
PDPM IIITDM Jabalpur
Jabalpur — 482005, Madhya Pradesh
Courses: Calculus · ODEs & PDEs · Linear Algebra & Probability · Numerical Methods
Recognition

Awards & Fellowships

🏆
ANRF National Post-Doctoral Fellowship (N-PDF)
Awarded by the Anusandhan National Research Foundation (ANRF) for a 2-year post-doctoral fellowship at IIT Ropar — a highly competitive national fellowship for research excellence.
🥇
Young Scientist Award — Mathematical Sciences
Conferred at the 37th M.P. Young Scientist Congress hosted by Mahatma Gandhi Chitrakoot Gramodaya Vishwavidyalaya, Chitrakoot. Includes a cash prize of ₹25,000.
🎓
INSPIRE Scholarship — DST, Government of India
Awarded during B.Sc. (2011–2014) and M.Sc. (2015–2017). Granted to students in the top 1% of Class XII board results, by the Department of Science and Technology.
🔬
INSPIRE Fellowship — DST
Provisional offer under INSPIRE Fellowship [DST/INSPIRE/03/2017/001914] to pursue research in basic and applied sciences.
📝
GATE 2018 & 2019 — Qualified
Qualified Graduate Aptitude Test in Engineering (Mathematics), organized by IITs and IISc on behalf of NCB-GATE, MHRD.
🧪
CSIR-UGC NET 2020 & 2021 — Qualified
Qualified the Joint CSIR-UGC National Eligibility Test in Mathematical Sciences conducted by the Council of Scientific & Industrial Research.
📐
JAM 2015 — Qualified
Qualified the Joint Admission Test for M.Sc. (Mathematics), conducted by IIT Guwahati, enabling admission to IIT Ropar for postgraduate studies.
🎖️
NCC Certificate ‘C’ — Ministry of Defence, GoI
Passed the Certificate ‘C’ Examination of the National Cadet Corps in 2013 under the authority of the Ministry of Defence, Government of India. Reg. No. UKSD/11/263463. Cert. Sl. No. UK/C Cert/Army/Boys/2013/17. Unit: 84 UK Bn NCC, Roorkee · NCC Directorate Uttarakhand.
🎖️
NCC Certificate ‘B’ — Ministry of Defence, GoI
Passed the Certificate ‘B’ Examination of the National Cadet Corps in 2012 under the authority of the Ministry of Defence, Government of India. Reg. No. UKSD/11/263463. Cert. Sl. No. UKSD/B Cert/Army/2012/0112. Unit: 84 UK Bn NCC, Roorkee · NCC Directorate Uttarakhand.
Beyond Research

Extracurricular Activities

🎤
First Prize — Mother Tongue Poetry & Song Competition
Awarded the first prize in the “Matrabhasha Kavita Path evam Geet Gayan Pratiyogita” (Faculty/Staff category) organised on the occasion of International Mother Language Day at IIT Ropar · 20 February 2026.
🇮🇳
First Prize — Patriotic Poetry & Song Competition
Awarded the first prize in the “Deshbhakti Kavita Path evam Geet Gayan Pratiyogita” (Faculty/Staff category) held at IIT Ropar to mark the 77th Republic Day · 20 January 2026.
🎭
Event Anchor — National Science Day 2024
Hosted the National Conference on Recent Trends in Physical Sciences (NCRTPS-2024) as an anchor — organised by the Natural Science Discipline (Mathematics), PDPM IIITDM Jabalpur, on the occasion of National Science Day · 28 February 2024.
🎶
First Prize — Patriotism Singing Competition
Awarded the first prize in the Patriotism Singing Competition held at IIT Ropar during M.Sc. studies (2016).
🥈
Second Prize — TARANG Cultural Festival
Secured the second prize for a singing band performance at TARANG, the annual cultural festival of PDPM IIITDM Jabalpur (2021).
🎙️
Solo Singing — ZIETGIEST Inter-College Fest
Participated in the Solo Singing competition at ZIETGIEST, the inter-college cultural festival of IIT Ropar (2017).
✍️
Essay Writing Competition — Prize Winner
Essay writing competition on the topic “Contributions of Indians towards the Freedom Struggle” held at PDPM IIITDM Jabalpur during Ph.D. · March 2021.
🏏
Cricket Team Member — M.Sc. & Ph.D.
Active member of the institute cricket team during M.Sc. at IIT Ropar and Ph.D. at PDPM IIITDM Jabalpur, representing the institutes in inter-college and institute-level fixtures.
🏏
FIT India Cricket Tournament 2022 — Century
Scored a century in the FIT India Cricket Tournament 2022 — the first ever by a Ph.D. scholar since the tournament's inception at IIITDM Jabalpur.
🏕️
NCC Combined Annual Training Camp (Pre-IGC)
Participated in National Cadet Corps Camp R-1361 CATC (Pre-IGC) at Birpur Cantt, Dehradun, from 29 Oct – 7 Nov 2011. Conduct rated Exemplary by the Camp Commandant.
🥾
All India NCC Shivaji Trail Trek 2012
Selected to represent the Uttarakhand Directorate at the All India NCC Shivaji Trail Trek held at Kolhapur, Maharashtra (20–27 Nov 2012) — a multi-stage trek across Panhala, Khutalwadi, Shahuwadi, Pandharpani, Gajapur and Vishalgarh.
Get in Touch

Let's Connect

Position
ANRF N-PDF Fellow, Department of Mathematics
Indian Institute of Technology Ropar
Address
Rupnagar, Punjab — 140001, India
Email
singh.harvindrahs@gmail.com
1915605@iiitdmj.ac.in
Mobile
+91-9027279494
Scholar
Google Scholar Profile ↗
ORCID
0000-0002-3032-4642

Open to Collaboration

My research lies at the intersection of numerical analysis, spectral methods, and the theory of partial differential equations. I focus on developing computationally efficient, high-order algorithms for nonlinear and fractional PDEs — particularly problems in fluid dynamics and mathematical physics.

I welcome research collaborations, visiting positions, and discussions on spectral methods for challenging PDE problems.