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Dr. Vineet Kumar Singh
Associate Professor
Department of Mathematical Sciences,IIT BHU.
vksingh.mat@iitbhu.ac.in
7376716701
Area of Interest: 
Numerical Wavelets Method for Integral Equations and Differential Equations, Operational Matrix Methods, Signal Processing

Education:

Ph. D.:  Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi.
Ph.D Thesis Title: Wavelets Based Techniques to Compute Hankel Transform and Operational Matrix Method for Abel’s Inversion and Certain Variational Problems
M. Sc. Mathematics: Udai Pratap Autonomous College Varanasi.
B. Sc. Mathematics: Udai Pratap Autonomous College Varanasi.

Postdoctoral Research Experience: 

Post-Doc Fellow ( BOYSCAST Fellow awarded by Department of  Science and Technology, India)  : Kursk State University, Kursk, Russia.

Current Position: 

Associate Professor in Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi:  July 19, 2017-till date.

Teaching Experience: 
1. Associate Professor in Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi:  July 19, 2017-till date.
2. Assistant Professor in Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi:  December 24, 2013 -July 18, 2017.
3. Assistant Professor in Department of Mathematics at National Institute of Technology, Kurukshetra since November 19, 2013 - December 23, 2013.
4. Assistant Professor in Department of Mathematics at Birla Institute of Technology and Science, Pilani (BITS-Pilani)-Goa Campus, Goa from: June 29, 2009 to November 18, 2013.
 

 

Courses Taught at Indian Institute of Technology (BHU) Varanasi

  • Engineering Mathematics I
  • Engineering Mathematics II
  • Mathematical Methods
  • Numerical Techniques
  • Integral Equations and Calculus of Variation
  • Algebra
  • Linear Algebra
  • Human Values

Research Areas:

  • Computational Approach for Integral Equations and  Differential Equations.
  • Numerical Wavelets Analysis 
  • Operational Matrix Methods.
  • Computational Approach for Fractional Mathematical Models
  • Signal Processing by Using Wavelets

International Pulications:

  1. V. K. Singh, O. P. Singh, R. K. Pandey, Efficient algorithms to compute Hankel transform using wavelets, Computer Physics Communications, 179 (2008) 812-818.
  2. V. K. Singh, O. P. Singh, R. K. Pandey, Numerical evaluation of Hankel transforms by using linear Legendre multi-wavelets, Computer Physics Communications179 (2008) 424-429. 
  3. V. K. Singh, R. K. Pandey, O. P. Singh, New stable numerical solutions of  singular integral equations of Abel type by using normalized Bernstein  polynomials, Applied  Mathematical  Sciences, Vol. 3 No. 5 (2008)441-455. 
  4. R. K. Pandey, O. P. Singh, V. K. Singh, An efficient algorithm for computing zero- order Hankel transforms, Applied Mathematical Sciences, Vol. 2 No.60(2008)2991-3000. 
  5. A. K. Singh, V. K. Singh , O. P. Singh, Bernstein operational matrix of integration, Applied Mathematical Sciences, Vol. 3, 2009, no. 49, 2427-2436.
  6. R. K. Pandey, O. P. Singh, V.K. Singh, Efficient algorithms to solve singular integral equations of Abel type, Computer & Mathematics with Applications, 57(4) (2009) 664- 676. 
  7. R. K. Pandey, V. K. Singh, O. P. Singh, An improved method for computing  Hankel transform, Journal of The Franklin Institute, 346 (2)(2009) 102-111. 
  8. O. P. Singh, R.K.Pandey, V. K. Singh, An analytic algorithm for Lane -Emden  equations arising in Astrophysics using MHAM, Computer Physics Communications, 180 (2009) 1116-1124. 
  9.  O. P. Singh, V. K. Singh, R. K. Pandey, A New Stable Algorithm for Abel   inversion Using Bernstein Polynomials, International Journal of Nonlinear  Sciences and Numerical Simulation, 10 (5) (2009) 681-685. 
  10. R. K. Pandey, O. P. Singh, V. K. Singh, Numerical solution of system of Volterra  integral equations using Bernstein polynomials, International Journal of  Nonlinear Sciences and Numerical Simulation 10 (7) (2009) 691-695. 
  11.  O. P. Singh, V. K. Singh, R. K. Pandey, New stable numerical inversion of  Abel's integral equation using almost Bernstein operational, Journal of Quantitative Spectroscopy and Radiative Transfer, 111 (2010) 245-252. 
  12. V. K. Singh, R. K. Pandey, A Stable Algorithm for Hankel transform using hybrid of Block pulse and Legendre polynomials, Computer Physics Communications181 (2010) 1-10 . 
  13. R. K. Pandey, O. P. Singh, V. K. Singh., A Stable Algorithm for Numerical     evaluation of Hankel transforms using Haar wavelet, Numerical Algorithms 53(4) (2010) 451-466.  
  14.  V. K. Singh, O. P. Singh, R. K. Pandey, Almost Bernstein Operational Matrix  Method For Solving Systems of Volterra Integral Equations of Convolution Type, Non Linear Sciences Letters A, 1 (2) (2010) 201-206. 
  15.  R. K. Pandey, V. K. Singh, O. P. Singh, A New Stable Algorithm for Hankel transform using Chebyshev Wavelets, Communications in Computational Physics 8(2) (2010) 351-373. 
  16.  R. K. Pandey, O. P. Singh, V. K. Singh, D. Singh,  Numerical evaluation of    Hankel transforms using Haar wavelets, International Journal of Computer Mathematics 87 (11) (2010) 2568-2573. 
  17.  O. P. Singh, V. K. Singh, R. K. Pandey, An efficient and stable algorithm for   numerical evaluation of Hankel transforms, Journal of Applied Mathematics & Informatics 28 (5-6) (2010) 1055-1071. 
  18. S. Dixit, V. K. Singh, A. K. Singh, O. P. Singh, Bernstein direct method for solving variational problems, International Mathematical Forum, Vol. 5, No (48), 2010, 2351-2370. 
  19. D. Singh, R. K. Misra, V. K. Singh, R. K. Pandey, Bad data pre-filter for state estimation, Electrical power and energy systems, Vol. 32 (2010) 1165-1174. 
  20. E. B. Postnikov, V.K. Singh, Local spectral analysis of images via the wavelet transform based on partial differential equations, Multidimensional system and signal analysis, DOI 10.1007/s11045-012-0196-1. 
  21. V. K. Singh, E. B. Eugene, Operational Matrix Approach for Solution of Integro-Differential Equation Arising in Theory of Anomalous Relaxation Processes in Vicinity of Singular Point, Applied Mathematica Modelling, 37(2013)6609-6616. 
  22. E. B. Postnikov, V. K. Singh, Continuous wavelet transform with the Shannon wavelet      from the point of view of hyperbolic partial differential equations, Analysis Mathematica, 51 (2015) 199-206. 
  23. S. Singh, V. K. Patel, V. K. Singh, Operational matrix approach for the solution of partial integro-differential equation, Applied  Mathematics and Computation, 283 (2016), 195-207. 
  24. C. S. Singh, H. Singh, V. K.  Singh, Om P. Singh, Fractional order operational matrix methods for fractional singular integro-differential equation, Applied Mathematical Modelling, 40 (2016)10705-10718. 
  25. S. Singh, V. K. Patel, V. K. Singh, E. Tohidi, Numerical Solution of Nonlinear weakly Singular Partial Integro-differential Equation via Operational Matrices, Applied Mathematics and Computation, Vol. 298 (2017), 310-321. 
  26. V. K. Patel, S. Singh, V. K. Singh, Two-Dimensional Wavelets Collocation Method for Electromagnetic Waves in Dielectric Media,  J. Appl. Math. Comput., Vol. 317 ( 2017), 307-330. 
  27. V. K. Patel, S. Singh, V. K. Singh, Two-Dimensional Shifted Legendre Polynomial Collocation Method for Electromagnetic Waves in Dielectric Media via Almost Operational Matrices, Mathematical Methods in the Applied Sciences, Vol. 40 (2017), 3698-3717. 
  28. S. Singh, V. K. Patel, V. K. Singh,  Application  of  wavelet collocation method for hyperbolic partial differential equation via  matrices, Applied  Mathematics  and Computation, 320 (2018) 407–424. 
  29. S. Singh, V. K. Patel, V. K. Singh, E. Tohidi, Application of Bernoulli matrix  method  solving  two-dimensional  hyperbolic  telegraph  equation  with Dirichlet boundary  conditions, Computer and  Mathematics with Applications,  https://doi.org/ 10.1016/j.camwa. 2017.12.003. 
  30.  S. Singh, V. K. Patel, V. K. Singh, A Study on Convergence rate of Collocation  Method  based  on  Wavelet  for  Nonlinear  weakly  Singular  Partial Integro-differential  Equation  Arising  from  Viscoelasticity, Numerical Methods for Partial Differential Equations, DOI: 10.1002/num.22245.
  31. V. K. Patel, V. K. Singh, E. B. Postnikov,  Application of Piecewise Expansion based on 2D Legendre Wavelets for Fractional Partial Differential Equation, International Journal of Pure and Applied Mathematics,  119 (2018), 5159-5167.
  32. V. K. Patel, S. Singh, V. K. Singh, E. Tohidi,  Two Dimensional Wavelets Collocation Scheme for Linear and Nonlinear Volterra Weakly Singular Partial Integro-Differential Equations, International J. of Applied and Computational Mathematics, https://doi.org/10.1007/s40819-018-0560-4.
  33. Vinita Devi, Rahul Kumar Maurya, Vijay Kumar Patel, Vineet Kumar Singh, Lagrange Operational Matrix Methods to Lane-Emden, Riccati’s and Bessel’s Equations, International Journal of Applied and Computational Mathematics, 2019, doi.org/10.1007/s40819-019-0655-6
  34. Rahul Kumar Maurya, Vinita Devi, Vineet Kumar Singh, Lagrangian Computational Matrix Approach to Generalized Abel’s Integral Equation based on Gauss Legendre Roots, Journal of Advanced Research in Dynamical and Control Systems, Vol. 11, 2019, Pages: 1717-1722
  35. Vinita Devi, Rahul Kumar Maurya, Somveer Singh, Vineet Kumar Singh, Lagrange’s operational approach for the approximate solution of two-dimensional hyperbolic telegraph equation subject to Dirichlet boundary conditions, Applied Mathematics and Computation, 367 (2020) 124717
  36. Somveer Singh, Vinita Devi, Emran Tohidi, Vineet Kumar Singh, An efficient matrix approach for two dimensional diffusion and telegraph equations  with Dirichlet boundary conditions, Physica A 545 (2020) 123784.
  37. Rahul Kumar Maurya, Vinita Devi, Nikhil Srivastava, Vineet Kumar Singh, An efficient and stable Lagrangian matrix approach to Abel Integral and Integro-Differential equations, Applied Mathematics and Computation 374 (2020) 125005.
  38. Rahul Kumar Maurya, Vinita Devi, Vineet Kumar Singh, Multistep schemes for one and two dimensional electromagnetic wave models based on fractional derivative approximation, Journal of Computational and Applied Mathematics,Volume 380 (2020) 112985.
  39. Yashveer Kumar, SomveerSingh, Nikhil Srivastava, AmanSingh, Vineet Kumar Singh, Wavelet approximation scheme for distributed order fractional differential equations, Computers and Mathematics with Applications 80 (2020) 1985–2017.
  40. Vijay Kumar Patel,  Somveer Singh, Vineet Kumar Singh, Numerical wavelets scheme to complex partial differential equation arising from Morlet continuous wavelet transform, 2021;37:1163–1199.
  41. Rahul Kumar Maurya, Vinita Devi, Vineet Kumar Singh, Stability and convergence of multistep schemes for 1D and 2D fractional model with nonlinear source term, Applied Mathematical Modelling 89 (2021) 1721–1746.
  42. Nikhil Srivastavam, Aman Singh, Yashveer Kumar, Vineet Kumar Singh,  Efficient numerical algorithms for Riesz-space fractional partial differential equations based on finite difference/operational matrix, Applied Numerical Mathematics, 161, (2021), 244-274.
  43. Yashveer Kumar, Vineet Kumar Singh, Computational approach based on wavelets for financial mathematical model governed by distributed order time-fractional partial differential equation, Mathematics and Computers in Simulation,Volume 190, December 2021, Pages 531-569.
  44. Nikki Kedia, Anatoly Alikhanov, Vineet Kumar Singh, Stable Numerical Schemes For Time-Fractional Diffusion Equation With Generalized Memory Kernel, Applied Numerical Mathematics,172 (2022) 546–565. 
  45. Kedia, N., Alikhanov, A.A., Vineet Kr. Singh  (2022). Numerical Methods for Solving the Robin Boundary Value Problem for a Generalized Diffusion Equation with a Non-smooth Solution, Mathematics and its Applications in New Computer Systems. MANCS 2021. Lecture Notes in Networks and Systems, vol 424. Springer, Cham. https://doi.org/10.1007/978-3-030-97020-8_20.
  46. Aman Singh, Nikhil Srivastava, Somveer Singh,Vineet Kumar Singh, Computational technique for multi-dimensional non-linear weakly singular fractional integro-differential equation, Chinese Journal of Physics (2022) https://doi.org/10.1016/j.cjph.2022.04.015.
  47. Nikhil Srivastava, Aman Singh, Vineet Singh, Computational algorithm for financial mathematical model based on European option, Mathematical Sciences (2022) DOI: 10.1007/s40096-022-00474-0.
  48. Rahul  Kumar Maurya, Vineet Singh, A high order adaptive numerical algorithm for fractional diffusion wave equation on non-uniform meshes, Numerical Algorithms- Accepted- 2022. 
  49. Poonam Yadav, B. P. Singh, Anatoly  A. Alikhanov, Vineet Kumar Singh , Numerical scheme with convergence analysis and error estimate for variable order weakly singular integro-differential equation, International Journal of Computational Methods- Accepted August 30, 2022.
  50. Nikhil Srivastava, Vineet Kumar Singh, L3 approximation for Caputo derivative and its application to time-fractional wave equation-(I),Mathematics and Computers in Simulation- Accepted October-2022

 PRESENTATION(Conferences/Symposium/talks)

1. V. K. Singh,  “Numerical wavelets method for system of singular Voltera integro-differential equation “July 8-15, 2012, International Conference on Wavelets and Applications at the Euler International Mathematical Institute, Saint Petersburg, Russia
2. V. K. Singh,  ” Numerical method for system of singular Voltera integro-differential equations.” August 13-21, 2014, International Congress of Mathematicians ( ICM-2014 ) , COEX, SEOUL, South Korea.
3. S. Singh, V. K. Singh, “Application of operational matrices based on orthogonal polynomials for the numerical solution of partial differential equation” in the international conference Operator Theory, Analysis, Mathematical Physics (OTAMP)" held at St. Petersburg, Russia, August 2-7, 2016.
4. S. Singh, V. K. Singh, “Application of operational matrices for the numerical solution of partial differential equations” in the International Conference on Mathematical Modeling and Simulation, (ICMMS-2016), held at Banaras Hindu University, Varanasi, August 29-31, 2016.
5. S. Singh, V. K. Singh, “Application of wavelet based approximation for the solution of partial integro-differential equation arising from viscoelasticity” in the International Conference of the Indian Mathematics Consortium (TIMC) in Cooper ation with American Mathematical Society, held at Banaras Hindu University, Varanasi, December 14-17, 2016
6. S. Singh, V. K. Singh, “Application of Chebyshev wavelet approximation for nonlinear partial differential equations arising from viscoelasticity” in the international conference “Constructive nonsmooth analysis and related topics” held at St. Petersburg, Russia, May 22-27, 2017.
7. S. Singh, V. K. Singh, “An efficient computational technique for the numerical solution of matrix hyperbolic equations of first order” in the “International Conference on Mathematical Modeling and Applied Sciences, ICMMAS'2017” held at St. Petersburg, Russia, July 24-28, 2017.
8.V. K. Patel, V. K. Singh, E. B. Postnikov,  "Application of piecewise expansion based on 2D Legendre wavelets for fractional partial differential equation" in the international conference on computational methods, simulation and optimization (ICCMSO-2018) held at Asian Institute of Technology. Bangkok, Thailand from June 22,  2018 to June 24, 2018.
9. Rahul Kumar Maurya, Vineet Kumar Singh, "Adaptive Lagrangian Approach for nonlinear weakly singular partial integro -differential equation " in International Workshop on Analysis and PDE held at Leibniz University Hannover, Germany, from Oct 08-10, 2018.
10. Vinita Devi, Vineet Kumar Singh "Spectral Scheme for Linear and Non-Linear Initial Value Problems" in international Workshop on Analysis and PDE held at Leibniz University Hannover, Germany from Oct 08-10, 2018.
11. Rahul Kumar Maurya, Vineet Kumar Singh "Lagrangian computational matrix approach to Generalized Abel’s Integral Equation based on Gauss-Legendre roots" in International Conference on Computational Methods, Simulation and Optimization held at Asian Institute of Technology, Bangkok, from Jan 11-13, 2019.

 

Projects:

1. The project entitled "Numerical methods for integral equations and differential equations by using Wavelets and operational Matrix" has been approved in year-2016 by     Science and Engineering Research Board (SERB), India.(Amount: Rs. 6,93,000.00) 
2. SEED Grant research proposal with entitled "Numerical wavelets method for signal analysis and fractional calculus".(Amount: Rs.9,05,689.00)  
3 Wavelets and their application in signal and image processing, has been approved under GIAN programe by MHRD -2017( Rs. 5,44,000/--).
4. International Travel Support (ITS) approved by SERB- File No : ITS/2019/005549. Amount: 2,15,000/-
5. The project  entitled "Wavelets Adaptive Schemes for Singular Integral Equations"- MTR/2021/000124 - has been approved by Science and Engineering Research Board (SERB) in year 2022 ( Amount: Rs. 6,00000/--) .
 

Research Guidance:

Ph.D. Supervision 

1. 
Mr. Somveer Singh
Numerical methods based on wavelets and operational matrices for partial differential equations and integral equations
Awareded-2018

2.
Mr. Vijay Kumar Patel
Applications of wavelets and operational matrices for partial differential equations and singular integral equations
Awarded-2018
 
3.
Ms. Vinita Devi
Numerical schemes based on matrix approach for mathematical models with integers and non0integers orders
  Awarded- 2021.
4
Mr. Rahul Kumar Maurya
Adaptive Wavelet Techniques to Integral Equations and Partial Differential Equations
Awarded- 2021

5
Mr. Nikhil Srivastava
Numerical Approach for Fractional Calculus
In Progress-July 2018

6.
Mr. Aman Singh
Numerical wavelets Scheme for Integral and Differential equations
In Progress-July 2018

7
Mr. Yashveer Kumar
Wavelets and Operational Matrix Approach for Fractional calculus
In Progress-July-2018

8. Nikki Kedia
Numerical Adaptive Scheme for Partial differential Eqiations and Integral Equations
In Progress- January 2019

9. Poonam Yadav
Numerical Adaptive Scheme for Singular Integral Equations 
In Progress- January -2019

10. Ms. Priyanka
Numerical Methods for Some Integral and Differential Equations 
In Progress- January-2019

11. Mr. Anant 
Numerical Schemes for Stochastic Partial Differential Equations
In Progress- January-2019

Supervised at the level of Post-doctoral (Ongoing-01)
 Dr. Somveer Singh joined on May 31, 2019  as National Board for Higher Mathematics (NBHM) Post-Doc fellow under my supervision. 
 Email ID: rathaurbhu.90@gmail.com 
Cell No. +91-9695909303

M. Tech. Supervision (Awarded: 4):
 

  • Vipul Sharma, 2015: A study on wavelet based feature extraction techniques for text independent automatic speaker verification.
  • Saurabh Kumar, 2015: Multi-wavelet and polynomial techniques for numerical solution of integro-differential equations.
  • Shreya Singh, 2016: Numerical methods to solve Hankel transform.
  • Rahul Singh Pahrwa, 2016: Numerical solutions for partial differential equations.

Administrative Experience

  • Admin Warden of Visvesvaraya Hostel, IIT(BHU) Varanasi
  • Warden of Morvi Hostel, IIT (BHU) Varanasi.
  • Member of the users committee for GRTA, IIT (BHU) Varanasi.
  • Faculty In-Charge of the Department during institute day, IIT(BHU) Varanasi.
  • Member of the DUGC, IIT(BHU) Varanasi.
  • Member of the DPGC, IIT(BHU) Varanasi.
  • Member, Faculty Forum IIT (BHU) Varanasi from 2018.

Awards: 

  • BOYSCAST Research Fellowship Award 2010-2011 (Awarded by Department of Science & Technology India) 
  • INSA Bilateral Exchange Programme-2012.

Conferences/Workshops/Short-term Course

  • Organized
    • Coordinator, Workshop on wavelets and their application in signal and image processing, December 21 - 25, 2017, Department of Mathematical Sciences, IIT (BHU) Varanasi, India (funded by MHRD, Govt. of India, under GIAN scheme).
    • Organized AICTE Short Term Course on Computational Methods for Integral and Differential Equations(CMIDE 18) during 10-16, 2018.

Workshop Attended:

1. Annual Foundation School (AFS II-2006 Pune) supported by TIFR &NBHM.
2. Instructional workshop on Wavelets Analysis ,  Dept. of Mathematics Banaras Hindu University Sponsored by DST New Delhi Oct 22 to Nov.5, 2007.

Short Visit :  July 27-August 9, 2016, at Kursk State University, Kursk, Russia.

 

PhD students and postdocs, having National Fellowships, are invited to join in the subject area of  computational Approach for PDEs and Integral Equations