Mathematics

Dr. Amit Kumar Verma

Dr. Amit Kumar Verma
Associate Professor
Ph.D, IIT KGP
Ph: +91-6115-233 396
akverma[*AT]iitp.ac.in
Research Areas
  • Nonlinear Singular Boundary Value Problems Epitaxial Growth Problems Non Standard Finite Difference Schemes Numerical Solutions of Nonlinear Partial Differential Equations Theory and Applications of Wavelets Integral Transforms
Courses taught at IIT P
  • MA001: Preparatory Mathematics MA101: Mathematics I (Advanced Calculus)* MA215: Real Analysis MA218: Complex Analysis MA231: Introduction to Numerical Methods MA421: Linear Algebra (Inner Product Spaces, Bilinear Forms) MA422: Topology MA428: Measure Theory and Integration MA425: Real Analysis MA430: Numerical Analysis MC594: Seminar MA511: Large Scale Scientific Computation (Parallel Computing, Multi Grid Analysis, Domain Decomposition) MA521: Functional Analysis MA540: Wavelets Transform MA632: Sobolev Spaces
PHD Students
Sr. No. Photo Area of Reasearch Status
1
Dr. Mandeep Singh: Monotone techniques for a class of nonlinear boundary value problems, 2011 - 2015. (Awarded)
2
Dr. Sheerin Kayenat: On the Stability and Convergence of Non-standard Finite Difference Schemes for a Class of Nonlinear ODEs and PDEs, 2016 - 2021. (Awarded)
3
Dr. Biswajit Pandit: On a class of nonlinear singular boundary value problems arising in epitaxial growth, 2017 - 2022 (Awarded)
4
Dr. Mukesh Kumar Rawani: On Stability and convergence of some novel numerical schemes for a class of nonlinear PDEs, 2016 - 2023 (Awarded)
5
Dr. Nazia Urus: Existence results for a class of nonlinear four-point BVPs in the presence of upper and lower solutions. 2017 - 2023 (Awarded)
6
Dr. Bivek Gupta: On A Class of Novel Generalized Fractional Integral Transforms and their Properties. (Awarded, 4 April 2024)
7
Navneet Kaur (2019-2024): On a Class of Integral Transforms and Their Uncertainty Principles. (Thesis submitted July, 2024).
Former PHD Students
Sr. No. Photo Area of Reasearch Current Position
1
Loknath Kannaujia: tba
2
Prabhat: TBA
3
Anikta Yadav
Current Sponsored Projects
Sr. No. Title Principal Investigator Co-Principal Investigator Duration Sponsoring Agency Cost Status
1 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]
2 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]
3 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.
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).
Publications / Journals / Conferences

  •  For complete list of publications click the link Click here for Full CV

    • Sarika Kumari, Loknath Kannaujia, Narendra Kumar, Amit K. Verma, Ravi P. Agarwal, A novel hybrid variation iteration method and eigenvalues of fractional order singular eigenvalue problems, Journal of Mathematical Chemistry, Springer (Accepted) https://doi.org/10.1007/s10910-024-01651-3
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    • Mukesh Rawani, Amit K. Verma, Carlo Cattani, An efficient algorithm for solving the variable-order time-fractional generalized Burgers’ equation, Journal of Applied Mathematics and Computing, Springer (Accepted). https://doi.org/10.1007/s12190-024-02177-2
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    • Mukesh Rawani, Amit K. Verma, Carlo Cattani, An efficient algorithm for solving the variable-order time-fractional generalized Burgers' equation, Journal of Applied Mathematics and Computing, Springer (Accepted). https://doi.org/10.1007/s12190-024-02177-2
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    • Bivek Gupta, Amit K. Verma, On a short time quaternion quadratic phase Fourier transform, Advances in Applied Clifford Algebras, Volume 34, article number 28, (2024) Springer. https://doi.org/10.1007/s00006-024-01334-x
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    • Bivek Gupta, Amit K. Verma, Linear Canonical Stockwell Transform and the associated Multiresolution Analysis, Mathematical Methods in Applied Sciences, Accepted, March 9, 2024, Wiley. https://doi.org/10.1002/mma.10072.
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    • Nazia Urus, Amit K. Verma, Existence results for a class of four point nonlinear singular BVP arising in thermal explosion in a spherical vessel, Mathematics and Computers in Simulation, Volume 220, June 2024, Pages 516-532 (Elsevier). https://doi.org/10.1016/j.matcom.2024.02.006.
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    • Bivek Gupta, Amit K. Verma, Ravi P. Agarwal, Uncertainty principles associated with the short time quaternion coupled fractional Fourier transform, Matematički Vesnik, Volume 76 , Issue 1-2 , 84-104, 2024. DOI: 10.57016/MV-XtlG4184.
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    • Mukesh Kumar Rawani, Amit K. Verma and Lajja Verma, Numerical treatment of Burgers’ equation based on weakly L-stable generalized time integration formula with the NSFD scheme, Applied Mathematics and Computation, Vol. 467 (2024) 128485 (Elsevier). https://doi.org/10.1016/j.amc.2023.128485.
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    • Narendra Kumar, Diksha Tiwari, Amit K. Verma, Carlo Cattani, Hybrid model for the optimal numerical solution of nonlinear ordinary differential systems, Computational and Applied Mathematics, Vo. 42, Article number: 322 (2023) (Springer). https://doi.org/10.1007/s40314-023-02468-7
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    • 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, Vol. 118 (2023) 106986 (Elsevier) doi.org/10.1016/j.cnsns.2022.106986.
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    • Biswajit Pandit, Amit K. Verma, Ravi P. Agarwal, Existence and non-existence results for a class of non-self-adjoint 4th order SBVPs arising in real life, Mathematical Methods in Applied Sciences, Vo. 46 (2023) 6077 – 6110 (Wiley). https://doi.org/10.1002/mma.8893.
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    • 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
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    • 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).
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    • 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).
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    • 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, Vol. 45 (2022) 1276-1298, https://doi.org/10.1002/mma.6905 (Wiley).
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    • 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).
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    • 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).
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    • 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).
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    • 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).
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    • 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).
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    • 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).
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    • 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).
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    • 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).
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    • 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.
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    • 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).
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    • 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).
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    • 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).
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    • 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).
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    • 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

    • 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.
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    • 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.
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    • 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.
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    • 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.
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    • 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.
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    • 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).
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    • 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.
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    • 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. 
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    • 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.
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    • Delivered an invited talk on 1st December 2020 on “Non-standard finite difference techniques” on the foundation day of MMMUT, Gorakhpur.
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    • 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).
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    • Invited Lecture on Matlab under TEQIP at LNJPIT Chapra on 29th January 2019.
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    • Guest lectures on Mathematica in Faculty Development Program organised at IIT (ISM) Dhanbad from 4-12-2017 to 9th Dec 2017.
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    • 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).
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    • 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.
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    • 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.
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