- About Me
- Teaching
- Research
- Publications
- Projects
- Research Guidance
- Administration
- Achievements
- Activities
- Open Position

**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:**

**V. K. Singh**, O. P. Singh, R. K. Pandey, Efficient algorithms to compute Hankel transform using wavelets,*Computer Physics Communications,*179 (2008) 812-818.**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*.**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*.*- 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*.* - A. K. Singh,
**V. K. Singh**, O. P. Singh, Bernstein operational matrix of integration,*Applied Mathematical**Sciences,*Vol. 3, 2009, no. 49, 2427-2436*.* - 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*.* - 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*.* - 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. - 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. - 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*.* - 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*.* **V. K. Singh**, R. K. Pandey, A Stable Algorithm for Hankel transform using hybrid of Block pulse and Legendre polynomials,*Computer Physics**Communications*181 (2010) 1-10*.*- 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. -
**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. - 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. - 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*.* - 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*.* - 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. - 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. - 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**.** **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**.**- 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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 - 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 - 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 - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - 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. - Rahul Kumar Maurya,
**Vineet Singh**, A high order adaptive numerical algorithm for fractional diffusion wave equation on non-uniform meshes, Numerical Algorithms- Accepted- 2022. - 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. - 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