Pursuing:- 

• 01

Completed:

• 06 (05-Single, 01-Joint)

Journal Publications  (last 10 years):

1. Ruchika Lochab, Vivek Kumar:  A Comparative Study of High Resolution Methods for Nonlinear Hyperbolic Problems, Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), 2022;102:e202100462.
2. Sudhakar Yadav, Vivek Kumar: A Prey-Predator Model Approach to Increase the Production of Crops: Mathematical Modelling and Qualitative Analysis, International Journal of Biomathematics, Vol.15, 7, 2022, 2250042 - (1-38) .
3. Kartikay Bharadwaj, Vivek Kumar: Finite Element Analysis of the Singularly Perturbed Parabolic Reaction-Diffusion Problems with Retarded Argument, Numer Methods Partial Differ Equ., 2022 (38) 997–1014.
4. Sudhakar Yadav, Vivek Kumar: A prey–predator model and control of a nematodes pest using control in banana: Mathematical modeling and qualitative analysis,  International Journal of Biomathematics,  Vol. 15, 1, 2022, 2150089-(1-31).
5. Vivek Kumar, G. Leugering, Singularly Perturbed Reaction--Diffusion Problems on a k-star graph, Mathematical Methods in the Applied Sciences, Vol. 44 (2021) 14874–14891.
6. Ruchika Lochab, Vivek Kumar, A New Reconstruction of Numerical Fluxes for Conservation Laws using Fuzzy Operators, International Journal for Numerical Methods in Fluids, accepted, Vol. 93 (2021) 1690–1711.
7. Ruchika Lochab, Vivek Kumar, An improved flux limiter using fuzzy modifiers for Hyperbolic Conservation Laws, Mathematics and Computers in Simulation 181 (2021) 16–37.
8. Ruchika Lochab, Vivek Kumar, Numerical Simulation of Hyperbolic Conservation Laws Using High Resolution Schemes with the Indulgence of Fuzzy Logic, NUMTA 2019, LNCS 11974, pp. 139–153, 2020, https://doi.org/10.1007/978-3-030-40616-5_11
9. Kashvi Srivastava, Mihir Ahlawat, Jaskaran Singh and Vivek Kumar, Learning Partial Differential Equations from Noisy Data using Neural Networks, Journal of Physics: Conference Series 1655 (2020) 012075, doi:10.1088/1742-6596/1655/1/012075
10. Charu Arora et.al.  A Delayed Prey–Predator System with Migration and Disease Infection, Int. J. Appl. Comput. Math (2020) 6:132.
11. Charu Arora, Vivek Kumar, Dynamics of Predator–Prey System with Migrating Species and Disease in Prey Population, Differ Equ Dyn Syst (Springer), 2020.
12. Charu Arora, Vivek Kumar, Dynamics of One-prey and Two-predator System Highlighting the Significance of Additional Food for Predators with Beddington–DeAngelis Functional Response, Differ Equ Dyn Syst (Springer), 2018.
13. Shashi Kant, Vivek Kumar, Effect of prey migration on a delayed stage-structured prey-predator dynamics, NONLINEAR STUDIES,  Vol. 25, No. 1, pp. 35-51, 2018.
14. Vivek Kumar, Balaji Srinivasan, A novel adaptive mesh for singularly perturbed parabolic convection diffusion problems, Differ Equ Dyn Syst (Springer), Vol 27, 1-3 ,203-220, 2019.
15. Shashi Kant, Vivek Kumar, Dynamics of a prey-predator system with infection in prey, Electronic J. of Differential equations, No. 209, 1-27, 2017.
16. Charu Arora, Vivek Kumar, Shashi Kant, Dynamics of a high-dimensional stage-structured prey–predator model, Int. J. Appl. Comput. Math (Springer), Vol. 3, 427-445, 2017.
17. Balaji S., Vivek Kumar, The versatility of an entropy inequality for the robust computation of convection dominated problems, Procedia Computer Science, Vol. 108C, 887-896, 2017.
18. Shashi Kant, Vivek Kumar, stability analysis of predator-prey system with migrating prey and disease infection in both species, Applied Mathematical Modeling, 2017, Vol.  42. 509-539.
19. Shashi Kant, Vivek Kumar, Dynamical behavior of a stage structured prey predator model, International Journal of Nonlinear Analysis and Applications (IJNAA), Vol. 7, No. 1, 2016, 231-241.
20. Vivek Kumar & Balaji srinivasan, An Adaptive Mesh Strategy for Singularly Perturbed Convection Diffusion Problem, Applied Mathematical Modelling, Applied Mathematical Modelling 39 (2015) 2081–2091
21. Shashi Kant, Vivek Kumar, A Stage Structured Eco-epidemiological Model with Disease in the Prey and Impulsive Effects, International Journal of Pure and Applied Mathematics, 2015, Vol. 102, No. 3. 447-472.
22. Vivek Kumar, Boundary Characterstic Orthogonal Polynomials for Singularly perturbed problems, International Journal of Pure and Applied Mathematics (IJPAM), vol. 75, No. 4 , 2012.
23. Vivek Kumar, High accurate solver for heat equation using modified equation approach, Indian Journal of industrial and applied mathematics ( IJIAM) , Vol. 3, No. 1, 44-55, 2012.
24. Romain, Benjamin, vivek, et.al,  Influence of waves on the Lagrangian acceleration in two dimensional turbulent flows, ESAIM Proceedings, Vol.32, 231-241, 2011.
25. Vivek Kumar, High accurate solver for heat equation using modified equation approach, AIP Conference Proceedings, ICNAAM, Greece - 2010, Vol. 1281, 562-565, 2010.
26. Vivek Kumar, High order compact finite difference scheme for singularly perturbed reaction diffusion problems on a new mesh of Shishkin type, Journal of Optimization Theory and Applications (JOTA), Vol. 143, 123-147, 2009.
27. Vivek Kumar, Mani Mehra, Wavelet optimized finite difference method using interpolating wavelets for self-adjoint singularly perturbed problems, Journal of Comput. and Appl. Math.(JCAM), Vol. 230, 803-812, 2009.
28. Vivek Kumar, Raghurama Rao, Composite scheme using localized relaxation non-standard finite difference method for hyperbolic conservation laws, Journal of Sound and Vibration, Vol. 311, 786-801, 2008.
29. Vivek Kumar, Kapil Sharma, An optimized b-spline method for solving singularly perturbed differential difference equations with delay as well as advance,  Neural, Parallel, and Scientific Computations, Vol. 16, 371-386, 2008.
30. Vivek Kumar, Solving singularly perturbed reaction diffusion problems using wavelet optimized finite difference and cubic spline adaptive wavelet scheme, International Journal of Numerical Analysis and Modeling, Vol. 5, 2, 270-285, 2008.

Book Chapters/ Proceeding papers:

1. Deepti Kaur, Vivek Kumar, "Numerical Solution with Special Layer Adapted Meshes for Singularly Perturbed Boundary Value Problems", Applied Mathematical Analysis: Theory, Methods, and Applications, 2019, Springer.
2. Shashi Kant, Vivek Kumar, Global Dynamics of an Eco-epidemiological Model, Applied Nonlinear Dynamics and Chaos 2014 (ANDC 2014), Behrampore, West Bengal, (Elsevier), 2015, 172-179. ISBN-978-93-5107-250-8.
3. Shashi Kant, Vivek Kumar, A Stage-structured Eco-epidemiological Model with Refuge, International Conference onMathematics and Computer Science 2015(ICMACS 2015), Kerala, (Narosa Publications), 2015, 80-85. ISBN-978-81-8487-456-3
4. Shashi Kant, Vivek Kumar, Delayed prey-predator system with habitat complexity and refuge, International Conference on Mathematical Sciences 2014(ICMS2014), 2014, 584-591(Elsevier). ISBN 978-93-5107-261-4
5. Shashi Kant, Vivek Kumar, Analysis of an eco-epidemiological model with migrating and refuging prey,Mathematical Analysis and its applications, Springer Proceedings in Mathematics and Statistics, Vol. 143, 2015, 17-36.
6. Shashi Kant, Vivek Kumar, The control for prey-predator system with time delay and refuge, Mathematics and Computing, Springer Proceedings in Mathematics and Statistics, Vol. 139, 2015, 339-348. 

Conference/Seminar/Symposium/Workshop organized/attended: 

1. Organized member, 4th International conference on “Recent Advances in theory, Computation and application of Differential Equations”, 21-23 Jan., 2019, SAU - Delhi.
2. ICMMC-2018 December 1-3, South Asian University, New Delhi.
3. ICM 2018, Rio De Janeiro, Brazil, August 1-9, 2018.
4. VII PDE, optimal design and numerics Conference, Centro de ciencias de Benasque, Spain, Aug. 20, Sept. 1, 2017.
5. ICCS 2017, ETH Zurich, June 12-14, Switzerland, 2017.
6. ICIAM 2015, Beijing China, 10-14 August, 2015.
7. An adaptive mesh strategy for convection diffusion problems, Modelling 2014, Czech Republic, June 2-6, 2014.
8. Boundary Characterstic Orthogonal Polynomials for Singularly perturbed problems, ICIAM 2011, Vancouver, Canada, July 18- 22, 2011
9. Multiscale methods for fluid and plasma turbulence: application to magnetically confined plasmas in fusion device, CIRM-Marseilles, France, April 21-25, 2008. (full funding from French Embassy, New Delhi)
10.  National conference on methods and models in computing (NCM2C-07), School of Computer and Systems Sciences, JNU, New Delhi, Dec. 13-14, 2007.
11. International congress on industrial and applied mathematics (ICIAM), Zurich, Switzerland, July 16-20, 2007, http://www.iciam07.ch/.
12. Solving boundary layers problems using adaptive wavelets, WAVE2006, EPFL, Lausanne, Switzerland, 10-14 July, 2006, http://wavelet.epfl.ch/
13. Solving singularly perturbed reaction diffusion problems using cubic spline adaptive wavelet scheme, SCA2006, Alberta, Canada, 18-21 May, 2006, http://www.ualberta.ca/ sca2006/
14. The Third Montreal scientific computing days, Montreal, Quebec, Canada, 25-26th Feb. 2006, http://www.crm.umontreal.ca/Comp06/indexen.html
15. Numerical sol. of singular boundary value problems using B-Spline, Proceeding Joint INDIA-AMS Mathematical Meeting, pp. 48, Dec. 17-20, 2003, IIsc. Bangalore, India, http://math.iisc.ernet.in/
16. On a B-spline method for a class of singular two-point boundary value problems, International Conference on Non-linear Phenomena, pp. 32, Jan 5-10, 2004, IIsc. Bangalore, India, http://math.iisc.ernet.in/.

Research Projects (Major Grants/Research collaborations):

• NBHM Project - Convection dominant diffusion problems: Numerical computations of adaptive meshes and error estimations , 2016-2019
• DST-SERC fast track project for young scientist costing Rs.12,48000 for three years (Title: Development of numerical techniques for hyperbolic conservation laws and boundary layers problems), 2009-2012 (completed).

Association with Professional Societies: SIAM, ISIAM

Invited Talks:

• Invited talk, Department of Mathematics, Ramanujan College (University of Delhi), Jan. 30, 2019.
• Resource person, workshop on Numerical Methods and Its Applications in various allied fields of Sciences, under the aegis of DBT-Star College Scheme, Deen Dayal Upadhyaya College, September 17-22, 2018.
• Invited talk, SHVAMA PRASAD MUKHERJI COllEGE (For Women), Sept. 5, 2018.
• Resource person, workshop on Differential Equations, Mathematical Modelling and Analysis (DEMMA),Deshbandhu College,University of Delhi, July 24- 29, 2018.
• Department of Mathematics, ARSD College, DU-Delhi, Feb. 1, 2018.
• Invited talk ,  A novel  adaptive approach for solving singularly perturbed problems , Friedrich-Alexander-Universität Erlangen-Nürnberg, July 20, 2017.
• Resouse person, DST-Inspire lecture at ITM meerut, August 10, 2016.
• Resouse person, DST-Inspire lecture at Institute of Applied Medicine and Research, Ghaziabad, Nov. 7-11, 2016.
• Resourse person, Faculty Development Program on Continuum Mechanics, JIIT Noida, July 18-23, 2016.
• Resourse person,” workshop on computational software-Matlab, March 18, 2016, K. R. Mangalam University, Gurgaon, India.
• Invited talk at International Conference on Current Trends in PDEs: Theory and Computations, 28-30th December, 2015, SAU, New Delhi.
• Resourse person ”Workshop on Computational Techniques for Differential Equations with MATLAB”, July 2-6, 2015, IIT Roorkee.
• Resourse person for NPDE, LNMIIT- Jaipur, June 1-6, 2015
• Resourse Person in the workshop at South Asian University, March 13-17, 2015.
• Resource person, DST Inspire Science Camp - 2013, Kirori Mal College, DU, Dec. 21-25, 2013. 
• Resource person, Hands on session on Matlab, 9 - 11 Feb. 2012, National workshop and Training Prog. on Differential equations and Math. Modeling, Lady Shri Ram College for women, DU.
• Wavelets and its applications, National seminar on the role of mathematics, Govt. college, Panchkula, March 5, 2011.
• Some adaptive techniques for solving singularly perturbed problems, TIFR center, IIsc campus, Bangalore, Sept. 19, 2006.
• Adaptive Multiresolution Wavelets and Splines Method for Singularly Perturbed Problems, Dept. of Computer Science, University of Toronto, Canada, 23rd September 2005, http://www.cs.toronto.edu/NA/seminars.html
• Adaptive wavelets scheme for solving singularly perturbed problems, Dept. of Mathematics and Statistics, University of Guelph, Canada, 14th Oct. 2005, http://www.mathstat.uoguelph.ca/

Any other information:

1. Recipient of research award by DTU, 2022.
2. Got full funding from Brazilian Govt. to attend ICM 2018, Aug. 1-9, 2018, Rio, Brazil.
3. Visiting Position in Friedrich-Alexander-Universität Erlangen-Nürnberg, June - Sept. 2017
4. Full financial support by NBHM to attend ICIAM 2015 in Beijing, China.
5. Full financial support by NBHM to attend ICIAM 2007 in Zurich- Switerzland, and ICIAM 2011 in Vancouver, Canada.
6. Consultancy for Indira-Gandhi National Open University (IGNOU), New Delhi.
7. Financial grant to attend, WAVE2006, EPFL, Lausanne, Switzerland, 10-14 July, 2006.
8.  Indo-French sandwich postdoctoral fellowship 2008, ENS, Paris.
9.  All India Graduate Aptitude Test (GATE) 2000 (December 2000 – December 2004)
10. Qualified Joint CSIR-UGC Eligibility for Lectureship-National Eligibility Test - 2000
11. Designed the Syllabi for four year B. Tech Program in Mathematics & Computing, DTU.
12. Winner of the Mathematical quizzes conducted by Dept. of mathematics IIT Roorkee, (1999, 2000)
13. Member of DPGC (Departmental post graduate Committee), Indian Institute of Technology Kanpur, 2002 - 2003
14. Assistant coordinator, Counseling service, Indian Institute of Technology Kanpur, 2003 - 2004
15. Senator, Student Gymkhana, Indian Institute of Technology Kanpur, 2003- 2004.
16. Winner of Snooker championship organized by Hall-IV, IIT Kanpur (2002).