Dr. Amit Kumar Verma

Video Lectures:IIT PAL Video LecturesResearch Areas:Monotone Iterative Techniques in Abstract Spaces, Upper and Lower Solution Techniques, Nonlinear Singular Boundary Value Problems, Multi Point Boundary Value Problems, Wavelet Transforms, Theoretical Numerical Analysis

Ph.D Students:

Completed:

1. Mandeep Singh, Title of the Thesis : Monotone techniques for a class of nonlinear boundary value problems, Jan 2011 - 29^th March 2016.

Ongoing:

2. Mukesh Kumar Rawani: Analytical & numerical results on nonlinear parabolic PDEs.
3. Biswajit Pandit: Analytical & numerical solutions of singular ODEs and nonlinear PDEs.
4. Sheerin Kayenat: On the theory of NSFD Methods and EFD Methods.
5. Nazia Urus: Monotone iterative technique: ODEs
6. Bivek Gupta: to be updated

Project Staff: Monika Singh

Professional Experience:Assistant Professor, BITS Pilani, July 2009 - Dec 2015Member 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.
• 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]

Short Term Course/ Workshop / Conference:

Teaching:

• MA101 : Mathematics I (Advanced Calculus)
• MA231 : Introduction to Numerical Methods
• MA421 : Linear Algebra (Inner Product Spaces, Bilinear Forms)
• MA422 : Topology
• MA428 : Measure Theory and Integration
• MA511 : Large Scale Scientific Computation (Parallel Computing, Multi Grid Analysis, Domain Decomposition)
• MA521 : Functional Analysis
• MA540 : Wavelets Transform
• MA632 : Sobolev Spaces

Publications:

Selected Publications (Peer Reviewed International Journals [30]):

Epitaxial Growth:

1. Amit K. Verma, Biswajit Pandit and Ravi P. Agarwal, On approximate stationary radial solutions for a class of boundary value problems arising in epitaxial growth theory, Journal of Applied and Computational Mechanics, DOI: 10.22055/JACM.2019.30982.1806.

Wavelets:

1. Amit K. Verma and Diksha Tiwari, Higher resolution methods based on Quasilinearization and Haar Wavelets on Lane-Emden Equations, Accepted, 2 October 2018, International Journal of Wavelets Multiresolution and Information Processing, Vol. 17, No. 3 (2019) DOI: 10.1142/S021969131950005X, [SCIE].

Non Standard Finite Difference Schemes:

1. 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, J. Math. Chem. 56 (2018), no. 6, 1667–1706.

Four Point BVPs: 

1. Nazia Urus, Amit K. Verma, Mandeep Singh, Some New Existence Results for a Class of Four Point Nonlinear Boundary Value Problems, JNPG-The Journal of Revelations, Vol. 3 (1), 7-13.
2. Amit K. Verma, Nazia Urus, Mandeep Singh, Monotone Iterative Technique for a Class of Four Point BVPs with Reversed Ordered Upper and Lower Solutions, International Journal of Computational Methods (World Scientific), https://doi.org/10.1142/S021987621950066X

Nonlinear Three Point BVPs:

1. Mandeep Singh, Amit K. Verma, Nonlinear three point Singular BVPs : A Classification, Communications in Applied Analysis, 21, No. 4 (2017), 513-532 ISSN: 1083-2564. 
2. Amit K. Verma, Mandeep Singh, A note on existence results for a class of three-point nonlinear BVPs, Mathematical Modelling and Analysis (Taylor & Francis Journal) Vol. 20, Issue 4 (2015) 457-470. [MCQ] [SCIE]
3. Amit K. Verma, Mandeep Singh, Singular Nonlinear 3 Point BVPs arising in Thermal Explosion in a Cylindrical Reactor, Journal of Mathematical Chemistry (Springer) Vol. 53 (2) (2015) 670-684. [MCQ] [SCI]
4. Mandeep Singh, Amit K. Verma, Ravi P. Agarwal, Maximum and anti-maximum principles for three point SBVPs and nonlinear three point SBVPs, Journal of Applied Mathematics and Computing( Springer), Vol. 47 (2015), no. 1-2, 249–263. [MCQ] 
5. Amit K. Verma, Mandeep Singh, Maximum principle and nonlinear three point singular boundary value problems arising due to spherical symmetry, Communications in Applied Analysis, Vol. 19 (2015) 175–190. [MCQ]
6. Amit K. Verma, Mandeep Singh, Existence Of Solutions For Three-Point BVPs Arising In Bridge Design, Electronic J. Differential Equation, Vol. 2014 (2014), No. 173, pp. 1-11, ISSN: 1072-6691, Published from Department of Mathematics, Texas State University-San Marcos, USA. [MCQ] [SCIE]
7. Mandeep Singh and Amit K. Verma, [Invited Article] Picard type iterative scheme with initial iterates in reverse order for a class of nonlinear three point BVPs, International Journal of Differential Equation (Hindawi), Volume 2013 (2013), Article ID 728149, 6 pages. [MCQ]
8. Mandeep Singh and Amit K. Verma, On a monotone iterative method for a class of three point nonlinear nonsingular BVPs with upper and lower solutions in reverse order, Journal of Applied Mathematics and Computing (Springer), Vol. 43 (2013) 99–114. [MCQ]

VIM, HPM etc.:

1. Mandeep Singh and Amit K. Verma, An effective computational technique for a class of Lane-Emden equations,  Journal of Mathematical Chemistry (Springer) Volume 54, Issue 1, (2016) 231-251. [MCQ] [SCI]
2. Mandeep Singh, Amit K. Verma, Ravi P. Agarwal, On an iterative method for a class of 2 point \& 3 point nonlinear SBVPs, Journal of Applied Analysis and Computation, Volume 9, Number 4, August 2019, 1242-1260 [SCIE]. 

Burgers' Equation:

1. 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. [MCQ] [SCIE]
2. K. Pandey, Lajja Verma and Amit K. Verma, Du Fort-Frankel finite difference scheme for Burgers' equation, Arabian Journal of Mathematics (Springer), Volume 2, (2013), 91–101. [MCQ]
3. K. Pandey, Lajja Verma and Amit K. Verma, L-stable Simpson's 3/8 Rule and Burgers' Equation, Applied Mathematics and Computation (Elsevier), Vol. 218 (2011) 1342–1352. [MCQ] [SCIE]
4. K. Pandey, Lajja Verma and Amit K. Verma, On a finite difference scheme for Burgers’ equation, Applied Mathematics and Computation (Elsevier), Vol. 215, Issue 6 (2009) 2206–2214. [MCQ] [SCIE]

Nonlinear Two Point BVPs:

1. 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 (Elsevier), Volume 17, Issue 12, December 2012, Pages 4551–4558. [MCQ] [SCIE]
2. Amit K. Verma, Ravi P. Agarwal and Lajja Verma, Bessel functions and singular BVPs arising in physiology in the presence of upper and lower solutions in reverse order, Journal of Applied Mathematics and Computing (Springer), Volume 39, Numbers 1-2 (2012), 445-457. [MCQ] 
3. 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. [MCQ] [SCIE]
4. R. K. Pandey and Amit K. Verma, [Invited Article] On a constructive approach for derivative dependent singular boundary value problems, International Journal of Differential Equations, (Hindawi) Vol. 2011 (2011), Article ID 261963, 16 Pages. [MCQ] 
5. Amit K. Verma and Lajja Verma, [Invited Article] Nonlinear singular BVP of limit circle type and the presence of reverse ordered upper and lower solutions, International Journal of Differential Equations, (Hindawi) Vol. 2011 (2011), Article ID 986948, 13 Pages. [MCQ]
6. Amit K. Verma, Monotone iterative method and zero's of Bessel functions for nonlinear singular derivative dependent BVP in the presence of upper and lower solutions, Nonlinear Analysis: Theory, Methods & Applications (Elsevier), Vol. 74, Issue 14, October 2011, Pages 4709-4717. [MCQ] [SCI]
7. R. K. Pandey and Amit K. Verma, On solvability of derivative dependent doubly singular boundary value problems, Journal of Applied Mathematics and Computing (Springer), Vol. 33 (2010) 489–511. [MCQ] 
8. R. K. Pandey and Amit K. Verma, Monotone method for singular BVP in the presence of upper and lower solutions, Applied Mathematics and Computation (Elsevier), Vol. 215 (2010) 3860–3867. [MCQ] [SCIE]
9. 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 (Elsevier), Vol. 71, Issues 7-8 (2009) 3477-3487. [MCQ] [SCI]
10. R. K. Pandey and A. K. Verma, Existence-uniqueness results for a class of singular boundary value problems-II, Journal of Mathematical Analysis and Applications (Elsevier), Vol. 338 (2008) 1387 – 1396. [MCQ] [SCI]
11. R. K. Pandey and A. K. Verma, Existence-uniqueness results for a class of singular boundary value problems arising in physiology, Nonlinear Analysis: Real World Applications (Elsevier), Vol. 9 (2008) 40 – 52. [MCQ] [SCIE]

Invited Talks:

• Delivered lecture on Matlab under TEQIP at LNJPIT Chapra on 29^th January 2019.
• Delivered an invited talk IET Sitapur in DST Inspire camp from 15^th June 2018 to 19th June 2018.
• Lecture on "Role of Mass Media in Teaching and Learning Process" on 13^th June 2010 for IGNOU at M.L.K. (PG) COLLEGE Balrampur.
• Learning Calculus with Mathematica is delivered in BBVP, Pilani on 16 August 2012 as part of celebration in BBVP as Mathematics Week.
• DST Inspire lecture (http://www.inspire-dst.gov.in/) on 14^th July 2013 in SRIMT BKT Lucknow on Calculus via Mathematica.
• DST Inspire lecture (http://www.inspire-dst.gov.in/) on 1^st August 2014 in IET Sitapur on Life of Euler, Gauss, Ramanujan and Numerical Integration.
• Calculus with Mathematica is delivered in BBVP, Pilani on 18 August 2014 as part of celebration in BBVP as Mathematics Week.
• On Mathematicians and Mathematica in Regional Science Congress at Jawahar Navodaya Vidyalaya Kajra, 13 NOV, 2014.
• Coordinated an event on behalf of BITS Pilani "INFINITY 14" at Aditya Birla World Academy, Mumbai on 21^st Nov 2o14.
• Inaugural lecture on GANIT Week on 16^th December 2014, in CEERI VIDYA MANDIR, PILANI.
• Address to Students during assembly and lecture on 17^th December 2014, in BIRLA SHISHU VIHAR, PILANI as part of GANIT Week.
• Address to Students on Valedictory of GANIT week on 22^nd December 2014, in BIRLA SCHOOL, PILANI.
• Lecture on Beamer and Thesis writing in National Workshop on LaTeX and MATLAB for beginners at BITS Pilani, Pilani, Rajasthan, India on dated 24-28 Nov 2014.
• 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: 30.01.2015  &  31.01.2015. Also acted as advisory board member of the conference.
• 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 dated:  05.06.2015.
• Chief Guest for inauguration of Regional Mathematics Olympiad Camp at Jawahat Navodaya Vidyalaya, Bikram, Patna on 02-10-2016 at 10.00 AM.
• Resource person at BBVP Pilani 15-16 April 2017 on the occasion of National Conference on Mathematics Googol 2017. A talk was delivered on Fermat's Last Theorem and life of Andrew Wiles.
• Resource person for National Workshop on Computational and Industrial Mathematics-2017 held at KIIT Bhubaneshwar from 16-21 May, 2017.
• Invited talk at KKC College, Lucknow on Monotone Iterative Technique on 24^th Nov 2017.
• Guest lectures on Mathematica in Faculty Development Program organised at IIT (ISM) Dhanbad from 4-12-2017 to 9-12-2017.
• Invited talk DST Inspire Camp at Gopinath PG College, Gazipur, UP, on 21 Dec 2017.