Dr. Mukesh Kumar Rawani (Faculty)


Dr. Mukesh Kumar Rawani

Assistant Professor,
Department of Basic Science

9546983654   |   [email protected]

Ph.D, IIT Patna
M.Sc, IIT(ISM) Dhanbad
Subject Expertise
Differential Equations, Numerical Analysis, Real and Complex Analysis, Linear Algebra, Calculus.
Area Of Research
Numerical Solutions of Nonlinear Partial Differential Equations, Non-Standard Finite Difference Schemes, Theory and Applications of Wavelets, Existence and Uniqueness of Solution of Differential Equations.
Professional Experience
Assistant Professor at Bhagalpur College of Engineering Bhagalpur, Bihar from Dec. 2023 to till date.
Lecture at Govt. Polytechnic Sheikhpura, Bihar from August 2018 to Dec. 2023.
Assistant Professor at Bengal College of Engineering and Technology, Durgapur, West Bengal from Feb. 2015 to June 2015.
List Of Publications
1. Mukesh Kumar Rawani, Amit K. Verma, Lajja Verma, Numerical treatment of Burgers’ equation based on weakly L-stable generalized time integration formula with the NSFD scheme, Applied Mathematics and Computation, Vol. 467 (2024) 128485 (Elsevier), DOI: https://doi.org/10.1016/j.amc.2023.128485
2. Mukesh Kumar Rawani, Amit K. Verma, Carlo Cattani, A novel hybrid approach for computing numerical solution of the time-fractional nonlinear one and two-dimensional partial integro-differential equation, Communications in Nonlinear Science and Numerical Simulation, Vol. 118 (2023) 106986, (Elsevier).DOI: doi.org/10.1016/j.cnsns.2022.106986.
3. Amit K. Verma and Mukesh Kumar Rawani, Numerical Solutions of generalized Rosenau- KDV-RLW equation by using Haar wavelet collocation approach coupled with NSFD scheme and quasilinearization, Numerical Methods for Partial Differential Equations, Vol. 39 (2023) 1085– 1107,(Wiley).DOI: https://doi.org/10.1002/num.22925.
4. Mukesh Kumar Rawani, Lajja Verma, Amit K. Verma, Ravi P. Agarwal, On a weakly L-stable time integration formula coupled with nonstandard finite difference scheme with application to nonlinear parabolic PDEs, Mathematical Methods in Applied Sciences, Vol. 45: 1276-1298. DOI:doi:10.1002/mma.7853 (Wiley).
5. Amit K. Verma, Mukesh Kumar Rawani, Carlo Cattani, A numerical scheme for a class of generalized Burgers’ equation based on Haar wavelet nonstandard finite difference method,Applied Numerical Mathematics, Volume 168, October, Pages 41-54, 2021, (Elsevier). DOI:https://doi.org/10.1016/j.apnum.2021.05.019.
6. Amit K. Verma, Mukesh Kumar Rawani, Ravi P. Agarwal, A novel approach to compute the numerical solution of variable coefficient fractional Burgers’ equation with delay,Journal ofApplied and Computational Mechanics, 7(3), 1550-1564, (2021), (Shahid Chamran University of Ahvaz, Iran).DOI: 0.22055/JACM.2021.35574.2689
7. Amit K. Verma, Mukesh Kumar Rawani, Ravi P Agarwal, A high-order weakly L-stable time integration scheme to solve Burgers’ equation, Computation, Vol.8(3), 72, 2020, (MDPI). DOI: https://doi.org/10.3390/computation8030072
8. Biswajit Pandit, Mukesh Kumar Rawani, Amit Kumar Verma, Carlo Cattani, Numerical approximation of higher order singular boundary value problem by using Haar function,Journal of Mathematical Chemistry, Vol.61(3), 539-568, 2023,(Springer).DOI: https://doi.org/10.1007/s10910-022-01421-z.
Conference Attended (National/International)
1. Amit K. Verma, Mukesh Kumar Rawani, Higher order numerical scheme with application on Burgers’ equation, National Conference of Recent Trends in Differential Equation: Theory, Modeling and Computation 2019(NCDE-2019),29-30 March 2019.
2. Mukesh Kumar Rawani, Amit K. Verma, On weakly L-stable higher order scheme with an application on Burgers’ equation, National Conference on Recent Advances in Physical Sciences, (NCRAPS-2019), R.N. College Hajipur (Vaishali), October 12-13,2019.
3. Mukesh Kumar Rawani, Amit K. Verma, On weakly L-stable time integration formulawith an application to non-linear parabolic partial differential equations, International Conference on Advances in Differential Equations and Numerical, Analysis (ADENA-2020), 12-15, Oct 2020, Indian Institute of Technology Guwahati, Department of Mathematics, Guwahati, India.
4. Mukesh Kumar Rawani, Amit K. Verma, A numerical scheme based on Haar waveletNSFD method for the solution of a class of generalized Burger’s equation, 86th Annual Conference of the Indian Mathematical Society, An International Meet (IMS 2020) 17-20, Oct 2020, School of advanced sciences Vellore institute of technology, Vellore.
Indian Mathematical Society (IMS): Life member.
Awards and Honors
CSIR-JRF in Mathematical Science with All India Rank-26, Dec-2015.
Qualified GATE in Mathematics-2015
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