1. Professor in School of Mathematics, Gangadhar Meher University, Odisha, March 2023 to till date.
2. Associate Professor in School of Mathematics, Gangadhar Meher University, Odisha, March 2020 to March 2023
3. Assistant Professor in Department of Mathematics, Sambalpur University, Odisha, Dec. 2012 to March 2020.
4. Visiting Faculty in Institute of Mathematics and Applications, Bhubaneswar, India, May 2012 - December 2012
5. Lecturer in Purushottam Institute of Engineering and Technology, Rourkela, Odisha, Jan 06 - July 2007

Research Area

1. Spectral Theory,
2. Numerical solutions of Integral Equations,
3. Non-linear Integral equations
4. Ill-posed Problems, Inverse Problems,
5. Integral equations of the first kind

Research Guidance

1. Subhashree Patel
2. Jitendra Kumar Malik M.Phil -15
P.G. -70

International Publications

1. S. Patel, B. L. Panigrahi, G. Nelakanti, Multi-projection methods for Fredholm integral equations of the first kind, International Journal of Computer Mathematics, 100(4), 722-744, 2023 [Index: WoS; Impact Factor: 1.8 ]
2. G. Long, G. Nelakanti, B. L. Panigrahi, M. M. Sahani, Discrete multi-projection methods for eigen-problems of compact integral operators. Applied Mathematics and Computation 217 (2010) 3974--3984. [Index: WoS; Impact Factor: 4 ]
3. B. L. Panigrahi, G. Nelakanti, Super-convergence of Legendre projection methods for eigenvalue problem of a compact integral operator. Journal of Computational and Applied Mathematics 235 (2011) 2380--2391. [Index: WoS; Impact Factor: 2.4 ]
4. B. L. Panigrahi, G. Nelakanti, Wavelet Galerkin Method for eigenvalue problem of a compact integral operator. Applied Mathematics and Computation 218 (2011) 1222--1232 [Index: WoS; Impact Factor: 4 ]
5. B. L. Panigrahi, P.D.Srivastava, Spectrum and fine Spectrum of generalized second order difference operator Delta^2_{uv} on sequence space c_0. Thai Journal of Mathematics 9 (2011) 57—74 [Index: WoS; Impact Factor: ]
6. B. L. Panigrahi, G. Nelakanti, Richardson extrapolation of iterated discrete Galerkin method for eigenvalue problem of a two dimensional compact integral operator. Journal of Scientific Computing 51 (2012) 421--448. [Index: WoS; Impact Factor: 2.5 ]
7. B. L. Panigrahi, P.D.Srivastava, Spectrum and fine Spectrum of generalized second order difference operator Delta^2_{uvw} on sequence space l_1. Demonstratio Mathematica 55 (2012) 593--609 [Index: WoS; Impact Factor: 2.0 ]
8. B. L. Panigrahi, G. Nelakanti, Legendre Galerkin method for weakly singular Fredholm integral equations and the corresponding eigenvalue problem. Journal of Applied Mathematics and Computing 43 (2013) 175--197. [Index: WoS; Impact Factor: 2.2 ]
9. B. L. Panigrahi, G. Long, G. Nelakanti, Legendre multi-projection methods for eigenvalue problem of a compact integral operator. Journal of Computational and Applied Mathematics 239 (2013) 135—151 [Index: WoS; Impact Factor: 2.4 ]
10. B. L. Panigrahi, Hybrid collocation methods for eigenvalue problem of a compact integral operator with weakly singular kernel, Applied Mathematics and Computation, 328 (2018) 353-364 [Index: WoS; Impact Factor: 4 ]
11. B. L. Panigrahi, Error analysis of Jacobi spectral collocation methods for Fredholm-Hammerstein integral equations with weakly singular kernel, International Journal of Computer Mathematics, 96(6), 1230–1253, 2019 [Index: WoS; Impact Factor: 1.8 ]
12. B. L. Panigrahi, M. Manadal, G. Nelakanti, Legendre multi-Galerkin methods for Fredholm integral equations with weakly singular kernel and the corresponding eigenvalue problem, Journal of Computational and Applied Mathematics, 346 224-236, 2019. [Index: WoS; Impact Factor: 2.4 ]
13. S. Patel, B. L. Panigrahi, Discrete Legendre spectral projection-based methods for Tikhonov regularization of first kind Fredholm integral equations, Applied Numerical Mathematics, 198, 75-93, 2024 [Index: WoS; Impact Factor: 2.8 ]
14. S. Patel, B. L. Panigrahi, Jacobi Spectral Projection Methods for Fredholm Integral Equations of the First Kind, Numerical Algorithms [Index: WoS; Impact Factor: 2.1 ]
15. S. Patel, B. L. Panigrahi, G. Nelakanti, Legendre Spectral Projection methods for Fredholm integral equations of First Kind, Journal of Inverse and Ill-posed Problems, 30(5), 677-691, 2022 [Index: WoS; Impact Factor: 1.1 ]
16. B. L. Panigrahi, Combined Legendre Spectral Finite element methods for two-dimensional Fredholm integral equations of the second kind, Numerical Functional Analysis and Optimization, 43(16), 1801-1820, 2022 [Index: WoS; Impact Factor: 1.2 ]
17. B. L. Panigrahi, Mixed Fourier Legendre spectral Galerkin methods for two-dimensional Fredholm integral equations of the second kind, Applied Numerical Mathematics, 168 (2021) 235–250 [Index: WoS; Impact Factor: 2.8 ]
18. S. Patel, B. L. Panigrahi, Legendre spectral projection methods for Hammerstein integral equations of mixed type, The Journal of Analysis, 28, 387-413, 2020. [Index: Scopus; Impact Factor: ]
19. S. Patel, B. L. Panigrahi, G. Nelakanti, Legendre spectral multi-projection methods for Fredholm integral equations of the first kind, Advances in Operator Theory, 7(4), 1-22, 2022 [Index: Scopus; Impact Factor: 0.8 ]
20. B. L. Panigrahi, J. K. Malik, Chebyshev spectral projection methods for Two-dimensional Fredholm integral equations of second kind, International Journal of Applied and Computational Mathematics, 7(70), 1-22, 2021. [Index: Scopus; Impact Factor: ]
21. B. L. Panigrahi, Galerkin methods for eigenvalue problem of an integral operator with logarithmic kernel, The Journal of Analysis, 25 (2) 235--251, 2017. [Index: Scopus; Impact Factor: ]
22. B. L. Panigrahi, Legendre spectral projection methods for Hammerstein integral equations with weakly singular kernel, International Journal of applied and Computational Mathematics, 4, 143 (2018). [Index: Scopus; Impact Factor: ]
23. B. L. Panigrahi, G. Nelakanti, Richardson extrapolation of iterated discrete collocation method for eigenvalue problem of a two dimensional compact integral operator. Journal of Applied Mathematics and Informatics 32 (2014) 567--584. [Index: UGC; Impact Factor: ]
24. J. K. Malik, B. L. Panigrahi, Jacobi spectral Galerkin methods for the eigenvalue problem of a compact integral operator, Acta Universitatis Apulensis, 61, 91-108, 2020. [Index: UGC; Impact Factor: ]
25. B. L. Panigrahi, Singularity preserving collocation methods for weakly singular Fredholm integral equations and the corresponding eigenvalue problem, International Journal of Convergence Computing, 2(3/4) 249—268, 2016. [Index: UGC; Impact Factor: ]
26. B. L. Panigrahi, J. K. Mailk, Discrete Legendre projection methods for the eigenvalue problem of a compact integral operator. Journal of Computer Science & Computational Mathematics, Volume 6, Issue 4, (2016), 81-89 [Index: UGC; Impact Factor: ]
27. J. K. Malik, B. L. Panigrahi, Discrete Chebyshev spectral projection methods for two dimensional Fredholm integral equations of the second kind, Journal of advanced Mathematical Studies, 13(1) 11-27, 2020 [Index: UGC; Impact Factor: ]
28. B. L. Panigrahi, Discrete Legendre multi-projection methods for Fredholm integral equations of the second kind and the corresponding eigenvalue problem, Communications in Numerical Analysis, 2018(2), (2018) 154-172. [Index: UGC; Impact Factor: ]
29. J. K. Malik, B. L. Panigrahi, Discrete Legendre projection methods for the Fredholm integral equations of the second kind, Indian Journal of Industrial and Applied Mathematics, 10 (2019) 38-50. [Index: UGC; Impact Factor: ]

International Conferences

1. Fourier Legendre spectral Galerkin methods for two-dimensional second kind Fredholm integral equations, International Conference on Advances in Pure and Applied Mathematics ICAPAM 2023, Ganpat University, Gujarat, 27-28 October 2023 [Index: ]
2. Hybrid collocation methods for Hammerstein integral equations with logarithmic kernel, 4th BRICS Mathematics Conference, IISER Thiruvananthapuram, 7-10 December 2021 [Index: ]
3. Chebyshev spectral projection methods for Fredholm integral equations of the second kind, 7th International Conference on Mathematics and Computing (ICMC-2021), IIEST Shibpur, 02-05 March, 2021 [Index: ]
4. Hybrid collocation methods for nonlinear integral equations with weakly singular kernel, International Conference on applied Nonlinear Analysis and Soft Computing, Department of Mathematics, Gauhati University, Guwahati-781014, 22-23 December 2020 [Index: ]
5. Chebyshev spectral projection methods for Fredholm integral equations of the second kind and the corresponding eigenvalue problem, JECRC University, Jaipur, Rajasthan, 8-10 August 2019, International Conference on Mathematical Modelling, Applied Analysis and Computation (ICMMAAC-19) [Index: ]
6. Hybrid collocation methods for eigenvalue problem of a compact integral operator, VIT Vellore, 13-15 Dec. 2018, Expert Talk, International conference on applications of fluid dynamics [Index: ]
7. Discrete Legendre collocation methods for Fredholm-Hammerstein integral equations with weakly singular kernel, Fourth International Conference on Mathematics and Computing 2018, Indian Institute of Technology (BHU) Varanasi, India, Jan 9-11, 2018 [Index: ]
8. Richardson extrapolation of discrete Projection method for eigenvalue problem of a two-dimensional compact integral operator. International Congress of Mathematicians (ICM), Hyderabad, India, August 19 -- 27, 2010. [Index: ]

National Conferences

1. Singularity preserving projection methods for eigenvalue problem of an integral operator with logarithmic kernel, National Conference on Engineering Mathematics (TOPAS-2017), Indian Institute of Technology Kharagpur, India, 16-17, December 2017 [Index: ]

Graduate Level:

1. Calculus
2. Real Analysis
3. Multivariate Calculus
4. An Introduction to MATLAB
5. Numerical Methods
6. Topology on Metric Spaces

Post Graduate Level:

1. Topology
2. Numerical Analysis
3. Functional Analysis
4. Wavelet Analysis
5. Operator Theory

Award, Honours and Achievements

1. Qualified GATE, Mathematics, 2007, joined IIT Kharagpur through MHRD Fellowship
2. Received Gold Medal for First class First in M.Sc., Sambalpur University, 2004
3. First Class FIrst in M.Phil, Mathematics, Sambalpur University, 2005
4. Best Tenth in B.Sc, Mathematics, Sambalpur University, 2002

Books / Chapters Published

1. Numerical solution of the Fredholm integral equations of the first kind by using Multi-projection Methods, Mathematics and Computing, Springer Proceedings in Mathematics and Statistics, 415, ISBN 978-981-19-9306-0, 978-981-19-9307-7 (eBook)
2. Chebyshev Spectral Projection Methods for Fredholm Integral Equations of the Second Kind, Proceedings of the Seventh International Conference on Mathematics and Computing, Advances in Intelligent Systems and Computing, vol 1412(2022)
3. Discrete Legendre collocation methods for Fredholm-Hammerstein integral equations with weakly singular kernel, Mathematics and Computing, ICMC 2018, Springer Proceedings in Mathematics and Statistics, Vol 253 (2018) 315-328, ISBN: 978-981-13-2095-8, Springer, Singapore

Sponsored Projects

1. Combined Legendre spectral finite element methods for integral equations, OURIIP Seed Grant, 2020, Rs. 3,30,000, Completed
2. Eigenvalue problem of a compact integral operator with weakly singular kernel and multigrid methods, DST, SERB, India, Rs. 7,22,800, 2013-2016, Completed

Members of Professional Bodies

1. Life Member, Indian Mathematical Society
2. Life Member, Mathematics Teachers Association
3. Life Member, Indian Science Congress
4. Life Member, Orissa Mathematical Society

Extra Responsibility

1. Head, School of Mathematics
2. Coordinator, Career Counselling and Placement Cell