Dr. Amit Kumar Verma
Dr. Amit Kumar Verma
Associate Professor
ORCID ID: 0000-0001-8768-094X
SCOPUS ID: 55574182537
Address: Dr. Amit Kumar Verma,
Chamber No. 319, Block 4, Department of Mathematics, IIT Patna,
Bihta, Patna - 801106, India.
Ph: +91-6115-233 396
Fax: +91-6115-233 7383
Click here for Full CV
Additional Responsibilities :
  • Associate Warden (1st April 2016 to 18th April 2017)
  • PIC Classroom and Time Table (April 2017 to April 2019)
  • DAPC Secretary (25th April 2018 till 24th April 2020)
  • PIC RSD 2019, 2021
  • Seminar Coordinator (2018-2022)
  • Social Media Coordinator Institute Innovation Committee (Since November 2021)
  • Senate Member IIT Patna 8 March 2022 - Till Date.
  • PIC - Central Exam Time Table and Classroom (August 2022 till date)
Courses Taught at IIT Patna :
  1. MA001: Preparatory Mathematics
  2. MA101: Mathematics I (Advanced Calculus)*
  3. MA231: Introduction to Numerical Methods
  4. MA421: Linear Algebra (Inner Product Spaces, Bilinear Forms)
  5. MA422: Topology
  6. MA428: Measure Theory and Integration
  7. MA425: Real Analysis
  8. MA430: Numerical Analysis
  9. MC594: Seminar
  10. MA511: Large Scale Scientific Computation (Parallel Computing, Multi Grid Analysis, Domain Decomposition)
  11. MA521: Functional Analysis
  12. MA540: Wavelets Transform
  13. MA632: Sobolev Spaces
Research Interests :
  1. Nonlinear Singular Boundary Value Problems
  2. Epitaxial Growth Problems
  3. Non Standard Finite Difference Schemes
  4. Numerical Solutions of Nonlinear Partial Differential Equations
  5. Theory and Applications of Wavelets
  6. Integral Transforms
Techniques Involved :
  1. Monotone Iterative Technique
  2. Upper and Lower Solutions
  3. Green's Function
  4. Eigenfunction Expansion
  5. Finite Difference Schemes, Homotopy Perturbation, Variation Iteration Scheme.
  6. Theory of Wavelets
  7. Nonstandard Finite Difference Schemes
  8. Integral Transform
Video Lectures : IIT PAL Video Lectures
Ph.D. Students (Submitted/Awarded) :  
Avijit Mandeep Singh: Monotone techniques for a class of nonlinear boundary value problems, Jan 2011 – March 2015. (Awarded)
Avijit Sheerin Kayenat: On the Stability and Convergence of Non-standard Finite Difference Schemes for a Class of Nonlinear ODEs and PDEs, August 2016 to October 2021. (Awarded)
Avijit Biswajit Pandit: On a class of nonlinear singular boundary value problems arising in epitaxial growth, 2017- 08th April 2022 (Awarded)
Mukesh Mukesh Kumar Rawani (2016-2022): On Stability and convergence of some novel numerical schemes for a class of nonlinear PDEs. (Synopsis Submitted on 18th August 2022).
Nazia Nazia Urus (2017-2022): Existence results for a class of nonlinear four-point BVPs in the presence of upper and lower solutions.(Synopsis Submitted on 31st August 2022).
Ph.D. Students (Ongoing) :
  1. Bivek Gupta: Harmonic Analysis (Theory of Wavelet Transforms)
  2. Navneet Kaur: Applications of Wavelets
  3. Loknath Kannaujia: tba
  4. Prabhat: TBA
  5. Vamika Rathi: TBA
M.Tech. Students :
  1. Gopal Jee Jha: Gopal Jee Jha : On Approximate Solution for a class of Boundary Value Problems via Fuzzy Transform, 2015-2016.
  2. Narendra Kumar: On the theory of Wavelets, 2019-20.
  3. Molkam Rakesh: Wavelets and Image Processing, 2020-21
MSc Students :
  1. Akash 2018
  2. Pandav Kumar Chaudhary 2018
  3. Naveen Kumar Mandal 2019
  4. Rohit Moundekar 2019
  5. Zabir Hussain 2020
  6. Dinesh Khati 2020
AMS Reviews : Reviewer for Mathematical Reviews® (MathSciNet®) since August 2012
Editorial Work : Working as editor of the following journals:
  1. Oriental Journal of Physical Sciences Online (ISSN: 2456-799X)
  2. Ganita (ISSN: 0046-5402)
Review for various journals :
  1. Applied Mathematics and Computation (Elsevier)
  2. Applied Numerical Mathematics (Elsevier)
  3. Journal of Applied Mathematics and Computing (Springer)
  4. International Journal of Applied and Computational Mathematics (Springer)
  5. Computational and Mathematical Methods (Springer)
  6. SpringerPlus (Springer)
  7. Journal of Mathematical Chemistry (Springer)
  8. Boundary Value Problems (Springer)
  9. Journal of Vibration Engineering & Technologies (Springer)
  10. Engineering Computations (Emerald)
  11. Numerical Methods for Partial Differential Equations (Wiley)
  12. Mathematical Methods in Applied Sciences (Wiley)
  13. Stochastics: An International Journal of Probability and Stochastic Processes (Taylor Francis)
  14. Arab Journal of Basic and Applied Sciences (Taylor & Francis)
  15. Proceedings of the National Academy of Sciences, India Section A: Physical Sciences (NASA)
  16. Proceedings of the National Academy of Sciences, Physical Sciences (NASA)
  17. Abstract and Applied Analysis (Hindawi)
  18. ANZIAM Journal
  19. Malaysian Journal of Mathematical Sciences
  20. Rocky Mountain Journal of Mathematics
  21. TWMS J. App. Eng. Math
  22. International Journal of Fluid Mechanics Research (Begell House Journals)
  23. Open Mathematics (Degruyter)
  24. Applied and Computational Harmonic Analysis (Elsevier)
  25. Mathematics and Computers in Simulation (Elsevier)
Professional Experience : Assistant Professor, BITS Pilani, July 2009 - Dec 2015
Assistant Professor, IIT Patna, December 2015 - February 2022
Associate Professor, IIT Patna, February 2022 - Till Date
Member of Professional bodies :
  • Student member (during Ph.D) of Society for Industrial and Applied Mathematics (SIAM).
  • Indian Mathematical Society (Life Member).
  • Bharat Ganita Parishad (Life Member).
Project :
  • SERB (DST, New Delhi) sanctioned ONE JRF + Travel + Contingency [Rs.16,51,680.00] for the Project Titled "Nonlinear Singular Differential Equations Arising in Real Life" for a period of three years. [Completed]
  • SERB (DST, New Delhi) sanctioned Rs 50000 as Seed Money (Travel+Contingency) against Project Titled "Nonlinear Singular Differential Equations Arising in Real Life " for the financial year 2014-2015. [Completed]
  • SERB (DST, New Delhi) sanctioned [Rs 6,60,000.00] a three-year MATRICS project titled "Offset linear canonical Stockwell transform". [On Going] File no. MTR/2021/000907.
Short Term Course/ Workshop / Conference :
Sr. No.TitleFunding AgencyFlyerYear
1. Monotone Iterative Technique MHRD under GIAN PDF 2017
2. Workshop on Sobolev Spaces CSIR, New Delhi PDF 2017
3. Modeling approaches of Nanoscale filtration processes of solutions and Suspensions MHRD under GIAN PDF 2016
4. Workshop on Fluid Mechanics DST SERB New Delhi India PDF 2016
5. Symposium on Modeling and Computation National Mathematics Initiative (DST), IISc Bangalore PDF 2016
6. NCDE 2019 DST(SERB), CSIR NCDE 2019
Publications :   For complete list of publications click the link Click here for Full CV
  1. Mukesh Rawani, Amit K. Verma, Carlo Cattani, A novel hybrid approach for computing numerical solution of the time-fractional nonlinear one and two-dimensional partial integro-differential equation, Communications in Nonlinear Science and Numerical Simulation, Accepted on 1st Nov 2022.
  2. Amit K. Verma and Mukesh Rawani, Numerical solutions of generalised Rosenau-KDV-RLW equation by using Haar wavelet collocation approach coupled with NSFD scheme and quasilinearisation, Numerical Solution of Partial Differential Equations, Accepted for publication on 7th Sep 2022. (Submitted on 28-Dec-2019) (Wiley).
  3. Mohammad Heydari, Nasibeh Karamollahi, Ghasem Barid Loghmani, Amit K. Verma, An explicit representation of the three-point Hermite interpolant for the numerical solution of singular boundary value problems, Applied Numerical Mathematics, Volume 182, December 2022, Pages 265-284 (Elsevier). https://doi.org/10.1016/j.apnum.2022.08.008
  4. Sheerin Kayenat, Amit K. Verma, On the choice of denominator functions and convergence of NSFD schemes for a class of nonlinear SBVPs, Mathematics and Computers in Simulation, Volume 200, October 2022, Pages 263-284, accepted 17th April 2022 (Elsevier).
  5. Amit K. Verma, Mukesh K. Rawani, Carlo Cattani, A numerical scheme for a class of generalized Burgers' equation based on Haar wavelet nonstandard finite difference method, Applied Numerical Mathematics, Volume 168, October, Pages 41-54, 2021, https://doi.org/10.1016/j.apnum.2021.05.019 (Elsevier).
  6. Amit K. Verma, Biswajit Pandit, Ravi P. Agarwal, Existence and nonexistence results for a class of fourth-order coupled singular boundary value problems arising in the theory of epitaxial growth, Mathematical Methods in Applied Sciences, Accepted (2021), https://doi.org/10.1002/mma.6905 (Wiley).
  7. Amit K. Verma, Sheerin Kayenat, Applications of Modified Mickens-Type NSFD Schemes to Lane-Emden Equations, Computational and Applied Mathematics, Vol. 39, Article No. 227, 2020, https://doi.org/10.1007/s40314-020-01257-w (Springer).
  8. Sawti, Karanjeet Singh, Amit K. Verma, Mandeep Singh, Higher order Emden-Fowler type equations via Uniform Haar Wavelet resolution technique, Journal of Computational and Applied Mathematics, Vol. 376, 112836, 2020, https://doi.org/10.1016/j.cam.2020.112836 (Elsevier).
  9. Amit K. Verma, Sheerin Kayenat, Gopal Jee Jha, A note on the convergence of fuzzy transformed finite difference methods, Journal of Applied Mathematics and Computing, Vol. 63, 143-170, 2020, https://doi.org/10.1007/s12190-019-01312-8 ( Springer).
  10. Amit K. Verma, Sheerin Kayenat, On the stability of Micken's type NSFD schemes for generalized Burgers Fisher equation, Journal of Difference Equations and Applications, Vol. 25, No. 12, 1706-1737, 2019, https://doi.org/10.1080/10236198.2019.1689236 (Taylor & Francis).
  11. Amit K. Verma and Sheerin Kayenat, On the Convergence of Mickens’ Type Nonstandard Finite Difference Schemes on Lane-Emden Type Equations, Journal of Mathematical Chemistry, 56 (2018), no. 6, 1667–1706, https://doi.org/10.1007/s10910-019-01013-4 (Springer).
  12. Mandeep Singh and Amit K. Verma, An effective computational technique for a class of Lane-Emden equations, Journal of Mathematical Chemistry, Vol. 54 (2016), no. 1, 231–251, https://doi.org/10.1007/s10910-015-0557-8 (Springer).
  13. Amit K. Verma, Lajja, Higher order time integration formula with application on Burgers' equation, International Journal of Computer Mathematics, Vol. 92 (No. 4) (2015) 756-771, https://doi.org/10.1080/00207160.2014.909032 (Taylor & Francis).
  14. Amit K. Verma and Ravi P. Agarwal, Upper and lower solutions method for regular singular differential equations with quasi-derivative boundary conditions, Communications in Nonlinear Science and Numerical Simulation, Volume 17, Issue 12, December 2012, Pages 4551–4558 https://doi.org/10.1016/j.cnsns.2012.03.027 (Elsevier).
  15. Amit K. Verma, The Monotone iterative method and regular singular nonlinear BVP in the presence of reverse ordered upper and lower solutions, Electronic J. Differential Equation, Vol 2012 (2012), No. 4, 1-10, ISSN: 1072-6691, Published from Department of Mathematics, Texas State University-San Marcos, USA.
  16. K. Pandey, Lajja Verma and Amit K. Verma, L-stable Simpson's 3/8 Rule and Burgers' Equation, Applied Mathematics and Computation, Vol. 218 (2011) 1342–1352, https://doi.org/10.1016/j.amc.2011.06.017 (Elsevier).
  17. Amit K. Verma, The monotone iterative method and zeros of Bessel functions for nonlinear singular derivative dependent BVP in the presence of upper and lower solutions, Nonlinear Analysis: Theory, Methods & Applications, Vol. 74, Issue 14, October 2011, Pages 4709-4717, https://doi.org/10.1016/j.na.2011.04.037 (Elsevier).
  18. R. K. Pandey and Amit K. Verma, Monotone method for singular BVP in the presence of upper and lower solutions, Applied Mathematics and Computation, Vol. 215 (2010) 3860–3867, https://doi.org/10.1016/j.amc.2009.08.018 (Elsevier).
  19. K. Pandey, Lajja Verma and Amit K. Verma, On a finite difference scheme for Burgers’ equation, Applied Mathematics and Computation, Vol. 215, Issue 6 (2009) 2206–2214, https://doi.org/10.1016/j.amc.2009.08.018 (Elsevier).
  20. R. K. Pandey and A. K. Verma, A note on existence-uniqueness results for a class of doubly singular boundary value problems, Nonlinear Analysis: Theory, Methods & Applications, Vol. 71, Issues 7-8 (2009) 3477-3487, https://doi.org/10.1016/j.na.2009.02.012 (Elsevier).
Invited Talks :    For complete list of talks click the link Click here for Full CV
  1. Delivered an invited talk on “Non-standard finite difference schemes”, at the International Conference on Dynamical Systems and Numerical Methods, Department of Mathematics, Jamia Millia Islamia, New Delhi-110025, India (ICDSNM-22), May 20-21, 2022.
  2. Delivered a talk titled “On some monotonic iterative schemes and upper-lower Solutions” as part of Drakhlin's Seminar on Functional Differential Equations, March 23, 2022 organized by Ariel University, Israel.
  3. Delivered a motivational talk on “Area and Surface Area” in Science Awareness Mela, organized during February 26th-28th, 2022 at Kunwar Inter College Narwar, Mardah Ghazipur.
  4. Delivered an Invited talk titled “Some new existence results for a class of nonlinear SBVP arising epitaxial growth” and chaired a session in Recent Developments in Engineering and Technology" (ICRDET-2022) February 25th-26th, 2022 at Anand International College of Engineering, Jaipur.
  5. Delivered a talk on “Polar Curves and Mathematica” at Centre for Applied Mathematics and Computing, Siksha ‘O’ Anusandhan Deemed to be University on 27th November 2021.
  6. Delivered a talk on “Mathematica and its applications” at an FDP organised by MMMTU, Gorakhpur, from 16-20 August 2021, Mathematical Tools and Recent Advances in Applied Mathematics (MTRAAM-2021) (Sponsored by AICTE Training and Learning Academy ATAL).
  7. Delivered a talk on “Classroom teaching: Learning Mathematical Methods for Engineering and Science Students” on Friday, 12 March 2021 organised by FDP by Jaipur National University, Jaipur.
  8. Delivered a talk titled “On the existence of solutions for a class of nonlinear singular BVPs arising in real life” as part of Drakhlin's Seminar on Functional Differential Equations, March 3rd 2021 organised by Ariel University. 
  9. Delivered a talk on 4th December 2020 on Numerical study of Stokes-Brinkman systems with varying liquid viscosity web conference “Membrane process modelling” in celebration of the 60th birth anniversary of Professor A.N. Filippov, Gubkin University, Russia.
  10. Delivered an invited talk on 1st December 2020 on “Non-standard finite difference techniques” on the foundation day of MMMUT, Gorakhpur.
  11. Delivered an invited talk on “Mathematica’’ on 22 September 2020, for the Faculty Development Program (21 September - 25 September) at Department of Mathematics and Scientific Computing, Madan Mohan Malaviya University of Technology, Gorakhpur, TEQIP-III sponsored, On Mathematical Tools and Recent Advances in Mathematics (MTAM-2020).
  12. Invited Lecture on Matlab under TEQIP at LNJPIT Chapra on 29th January 2019.
  13. Guest lectures on Mathematica in Faculty Development Program organised at IIT (ISM) Dhanbad from 4-12-2017 to 9th Dec 2017.
  14. Resource person at BBVP Pilani 15-16 April 2017 on the occasion of National Conference on Mathematics, Googol 2017. A talk was also delivered on Fermat's Last Theorem and the life of Andrew Wiles. (Prof. Govindan Rangarajan, IISc Bangalore also delivered a talk as Chief Guest of the event).
  15. Invited talk at ICMBAA 2015 AMU Aligarh, titled "A Review on Monotone Iterative Technique Related to Upper and Lower Solutions for a Class of Nonlinear Boundary Value Problems, on 5th June 2015.
  16. Invited talk at UGC sponsored National Conference on Applied Mathematics: Numerical analysis, Algebra & Computational Mathematics, Gudleppa Hallikeri College, Haveri, Karnataka, titled "Monotone Iterative Technique for a Class of Boundary Value Problems: A Review", on dated: 30th Jan 2015 & 31st Jan 2015. I also acted as an advisory board member of the conference.