Education

• Ph.D. (IIT Guwahati)
• M.Sc. (Visva-Bharati University, WB)
• B.Sc.  (Visva-Bharati University,WB)

Experience

• Associate Professor at Indian Institute of Space Science and Technology (IIST), Thiruvananthapuram, Jan 2017-Till date.
• Assistant Professor at Indian Institute of Space Science and Technology (IIST), Thiruvananthapuram, Sep 2011- Dec 2016.
• Reader at Indian Institute of Space Science and Technology (IIST), Thiruvananthapuram, Jun 2010-Sep 2011.

Research Work / Area

• Fitted-Mesh methods (FDM/FEM) for singularly perturbed PDEs/ODEs
• Fractional-step methods for multi-dimensional PDEs.
• Computational methods for PDEs with non-smooth data.
• Computational methods for Delay Differential Equations. 
• Numerical Analysis of nonlinear singular perturbation problems.

Area of Interest

Computational Methods and Analysis of Partial Differential Equations

Awards

• Recipient of National Board of Higher Mathematics (NBHM) Travel Grant Award to perticipate International Congress on Industrial and Applied Mathematics (ICIAM-2015), Beijing, China.
• Recipient of Department of Space (DoS) Travel Grant Award to to perticipate International Conference on Numerical Analysis and Applications (NAA-2022), Lozenetz, Bulgaria.
• Recipient of Post-doctoral Fellowship by NBHM, Department of Atomic Energy (DAE), Govt. of India, 2010.
• Recipient of Graduate Aptitude Test in Engineering (GATE) Scholarship, Ministry of Human Resource Development (MHRD), Govt. of India, 2004.
• Recipient of National Scholarship for M.Sc. by Govt. of West Bengal, India (July 2002-June 2004).
• Secured University First Rank in M.Sc. (Mathematics), Visva-Bharati University, Santiniketan, India, 2004.

•  IIST-IRINS Profile Link

17. N.S. Yadav and K. Mukherjee. Stability and Error Analysis of An Efficient Numerical Method for Convection Dominated Parabolic PDEs with Jump Discontinuity in Source Function on Modified Layer-Adapted Mesh. Computational Mathematics and Mathematical Physics, 2023, (In Press).

16. N.S. Yadav and K. Mukherjee. Higher-Order Uniform Convergence and Order Reduction Analysis of A Novel Fractional-Step FMM for Singularly Perturbed 2D Parabolic PDEs with Time-Dependent Boundary Data. Journal of Applied Analysis and Computation, 2023, (In Press).

15. N.S. Yadav and K. Mukherjee. Efficient Parameter-Robust Numerical Methods for Singularly Perturbed Semilinear Parabolic PDEs of Convection-Diffusion Type. Numerical Algorithms, 2023.

14. S. Bose and K. Mukherjee. A Fast Uniformly Accurate Global Numerical Approximation to Solution and Scaled Derivative of System of Singularly Perturbed Problems with Multiple Diffusion Parameters on Generalized Adaptive Mesh. Comp. Appl. Math. 42, 180, 2023.

13. S. Bose and K. Mukherjee. Numerical Approximation of System of Singularly Perturbed Convection-Diffusion Problems on Different Layer-Adapted Meshes. Smart Innovation, Systems and Technologies (SIST). 292, 523-535, 2022.

12. N.S Yadav and K. Mukherjee. An Efficient Numerical Method for Singularly Perturbed Parabolic Problems with Non-smooth Data. Communications in Computer and Information Science (CCIS). 1345, 159-171, 2021.

11. N.S Yadav and K. Mukherjee. On ε-Uniform Higher Order Accuracy of New Efficient Numerical Method and Its Extrapolation for Singularly Perturbed Parabolic Problems with Boundary Layer. Int. J. Appl. Comput. Math. 7: 72, 2021.

10. N.S Yadav and K. Mukherjee. Uniformly Convergent New Hybrid Numerical Method for Singularly Perturbed Parabolic Problems with Interior Layers. Int. J. Appl. Comput. Math., 6 (2), Paper No. 53, 44 pp., 2020.

9. K. Mukherjee and S. Natesan. Parameter-uniform fractional step hybrid numerical scheme for 2D singularly perturbed parabolic convection-diffusion problems. Journal of Applied Mathematics and Computing, 60(1-2), 51-86, 2019.

8. K. Mukherjee. Parameter-uniform improved hybrid numerical scheme for singularly perturbed problems with interior layers. Mathematical Modelling and Analysis, 23(2):167-189, 2018.

7. K. Mukherjee and S. Natesan.Uniform convergence analysis of hybrid numerical scheme for singularly perturbed problems of mixed type. Numerical Methods for Partial Differential Equations, 30(6):1931-1960, 2014.

6. K. Mukherjee and S. Natesan. An efficient hybrid numerical scheme for singularly perturbed problems of mixed parabolic-elliptic type. Lecture Notes in Computer Science (LNCS), 8236: 411-419, 2013.

5. K. Mukherjee and S. Natesan. ε-Uniform error estimate of hybrid numerical scheme for singularly perturbed parabolic problems with interior layers. Numerical Algorithms, 58:103-141, 2011.

4. K. Mukherjee and S. Natesan. Optimal error estimate of upwind scheme on Shishkin-type meshes for singularly perturbed parabolic problems with discontinuous convection coefficients. BIT Numerical Mathematics, 51(2):289-315, 2011.

3. K. Mukherjee and S. Natesan. Richardson extrapolation technique for singularly perturbed parabolic convection-diffusion problems. Computing, 92(1):1-32, 2010.

2. K. Mukherjee and S. Natesan. Parameter-uniform hybrid numerical scheme for time-dependent convection-dominated initial-boundary-value problems. Computing, 84(3-4):209–230, 2009.

1. K. Mukherjee and S. Natesan. An efficient numerical scheme for singularly perturbed parabolic problems with interior layers. Neural, Parallel, and Scientific Computations, 16:405–418, 2008.

Talks/Participation in Referred Conferences: 

1. Delivered a talk “On Fitted Mesh Methods for Singularly Perturbed Semilinear Parabolic PDEs”, in ``National Conference on Applied Mathematics and Numerics” (NCAMN), held at Mar Ivanios College, Trivandrum, during March 8–10, 2023.
2. Participated in  “International conference on Advances in Differential Equations and Numerical Analysis” (ADENA)-2020, held at IIT Guwahati, during Oct 12-15, 2020.
3. Participated in  “National conference on Stochastic Differential Equations and Applications” (CSDEA) 2019, held at IIST, Trivandrum during June 6-7, 2019.
4. Delivered a talk "A robust hybrid numerical scheme for a system of singularly perturbed convection-diffusion boundary-value problems", in ``International Conference on Advances in Scientific Computing" (ICASC 2016), to be held at IIT Madras, Chennai, during November 28-30, 2016.
5. Delivered a talk “A post-processing technique for singularity perturbed parabolic convection-diffusion problems on Shishkin-type meshes”, in ``National Conference on Emerging Trends in Mathematics and Mathematical Sciences", held at Calcutta Mathematical Society, Kolkata, December 17-19, 2015.
6. Participated in ``International Congress on Industrial and Applied Mathematics" (ICIAM-2015), held at Beijing, China, Aug 10-14, 2015.
7. Delivered a talk “Uniformly convergent numerical method for 2D Singularly Perturbed Problems”, in ``International Conference on Emerging Trends in Applied Mathematics", held at Department of Mathematics, University of Calcutta, February 12-14, 2014.
8. Delivered a talk “Efficient Numerical Scheme for 2D Singularly Perturbed Parabolic Convection-Diffusion Problems”, in ``National Conference on Analysis and Differential Equations "(NCFADE-2012), held at Department of Mathematics, Bharathidasan University, Tiruchirappalli, December 19-20, 2012.
9. Delivered a talk “Hybrid numerical scheme for singularly perturbed problems of mixed parabolic-elliptic type”, in ``Fifth Conference on Numerical Analysis and Applications"(NAA’12), held at Lozenetz, Bulgaria, June 15-20, 2012, organized by Division of Numerical Analysis and Statistics, University of Rousse, Rousse,Bulgaria.
10. Delivered a talk “A unified approach for uniform convergence of upwind scheme on Shishkin type meshes for singularly perturbed parabolic problems”, in `` International Conference on Advances in Modelling, Optimization and Computing "(AMOC-2011), held at Department of Mathematics, Indian Institute of Technology, Roorkee, December 5-7, 2011. 

Talks in Workshops/ Summer Schools/Fuculty Development Programmes:

1.  On “Differential equations and its applications”, in a two-day workshop on "Theory and Numerics of Differential Equations", held at Department of Mathematics, IIST, Trivandrum,  March 16–17, 2023.
2. On “Multivariable Calculus”, in “Faculty Development Programme” in Mathematics, organized by Human Resource Development Centre (HRDC), University of Kerala, held at Kariavattom Campus, Trivandrum, Sept 17 -Sept 30, 2019.
3. On “System of linear equations”, in “five-day NuMATS (Nurturing Mathematical Talents in Schools) camp” sponsored by the State Council of Educational Research and Training (SCERT), Government of Kerala, held at Department of Mathematics, IIST, Trivandrum, June 14- June 18, 2019.
4. On “Complex Analysis”, in “Young Talent Nurture-2019” programme, held at Department of Mathematics, IIST, Trivandrum, May 20- June 01, 2019.
5. On “Linear Algebra”, in “Young Talent Nurture-2018” programme, held at Department of Mathematics, IIST, Trivandrum, May 14- May 26, 2018.
6. On “Linear Algebra”, in AICTE sponsored “Short Term Course on Applied Mathematics for Engineering Research” organized by CET-Centre for Interdisciplinary Research, held at College of Engineering Trivandrum, Trivandrum, Dec 11, 2017.
7. On “Linear Algebra”, in “Young Talent Nurture-2017” programme, held at Department of Mathematics, IIST, Trivandrum, May 22-June 3, 2017.
8. On “Introduction to MATLAB”, Pratibha Summer Training Programme sponsored by KSCSTE (Kerala State Council for Science, Technology and Environment), held at IIST, Trivandrum, May 23-27, 2016.
9. On “Second-order differential equations”, NPDE-TCA (National Programme on Differential Equations- Theory Computation and Application) sponsored undergraduate level training programme, held at IIST, Trivandrum, May 18-June 7, 2016.
10. On “Second-order partial differential equations,”  in “Young Talent Nurture-2016” programme , held at Department of Mathematics, IIST, Trivandrum, May 24-June 6, 2016.
11. On “Fourier series and its applications”, TEQIP (Technical Education Quality Improvement Programme) sponsored workshop on Differential equations and its applications, held at College of Engineering, Karunagapally, Kerala, Feb 25-27, 2016.
12. On “Linear Algebra”, in “Young Talent Nurture-2014” programme, held at Department of Mathematics, IIST, Trivandrum, May 13-25, 2014.
13. On Linear Algebra”, in “Young Talent Nurture-2013” programme, held at Department of Mathematics, IIST, Trivandrum, for the 1st year B.Sc, B.Tech and integrated M.Sc students with Mathematics as one of their subjects of study, May 28-June 8, 2013. 

Participation in International Workshops :

1. Instructional pre-school and CIMPA research school on “Current Trends in Computational Methods for PDEs“, held at Department of Mathematics, IISc Bangalore during June 24-july 7 and July 8-19, 2013.
2. International Workshop on “Multi-scale Analysis and Homogenization”, held at Department of Mathematics, IISc Bangalore during June 28-July 10, 2010.

1. Act as a convenor of ``National Conference on Applied Mathematics and Numerics" (NCAMN) , held at Mar Ivanios College, Trivandrum, March 8- 10, 2023.
2. Act as an organizer of  ``International Mini-Symposium on Recent trends in Computational Methods for Singularly Perturbed Differential Equations”, which was the part of the international conference ``International Conference on Advances in Differential Equations and Numerical Analysis" (ADENA-2020), IIT Guwahati, Oct 12-15, 2020. 
3. Act as a convenor of the summer school ``Young Talent Nurture" (YTN-2019) programme, held at IIST, Trivandrum, May 20- June 01, 2019.
4. Act as a convenor of the summer school ``Young Talent Nurture" (YTN-2017) programme, held at IIST, Trivandrum, May 22- June 3, 2017.
5. Act as a convenor of the summer school ``Young Talent Nurture" (YTN-2016) programme, held at IIST, Trivandrum, May 24- June 06, 2016.
6. Act as a convenor of the workshop on ``Differential Equations and its Applications" (WDEAP-2013), held at IIST, Trivandrum, Dec 18-21, 2013.

MA221-Complex Analysis (January-April 2015): Syllabus

MA211-Fourier series, Fourier transforms and Laplace transforms (August-November 2014): Syllabus

Assignment: Assignment_FT-LT

Solve the assignment problems in A-4 size paper.

Date of submission:  27.08.2014 & Time: 12.00 hr.

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MA121-Differential Equation (January-April 2014): Syllabus

Lecture Notes:

Exact-DE & Integrating-Factor

Linear & Bernoulli-EQ 3. Lipschitz-Condition

Method of Successive Approximation

Existence-Uniqueness of IVP-1

Existence-Uniqueness of IVP-2

Non-local Existence Theorem

Linearly dependent-independent & Homogeneous Linear DE

Non-homogeneous Linear DE

Cauchy-Euler Eqn 11. Series Solution

Bessel eqn-1 13. Bessel eqn-2 14. Gamma Function 15. Sturm-Liouville  BVP

Assignments:

assignment_Vector-Calculus-2014 and assignment_DiffEq_2014

Solve the assignment problems in A-4 size paper.

Date of submission:  24.04.2014 & Time: 10 am.

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MA211-Linear Algebra (August-November 2013):

Solution of Prob No.16 in Tutorial-2:solution1

Lecture Notes: 1. Projection  2. Gram-Schimdt

Assignment-1 : solve 5(a) (forward part) and 15(c) (i) of Tutorial-1 in an A-4 size paper.

Date of submission:  17.09.2013

Assignment-2 : solve 1(a) and 12(b) of Tutorial-2 in an A-4 size paper.

Date of submission:  23.09.2013

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Courses offered in previous semesters:

1. Undergraduate (B.Tech):

    Integral and Vector Calculus
    Ordinary Differential Equations
    Linear Algebra
    Complex Analysis
    Fourier Series and Integarl Transforms
    Basic Programming Lab

2.  Postgraduate (M.Tech): Graph Theory

• Syllabus
• Syllabus
• Assignment_FT-LT
• MA121-Differential Equation-syllabus
• assignment_Vector-Calculus-2014
• solution1
• Projection
• Gram-Schimdt

Completed PhD student

Dr. Narendra Singh Yadav, Title of Thesis: Study of Higher-Order Fitted Mesh Methods for Singularly Perturbed Parabolic PDEs with Smooth and Nonsmooth Data, 2022.

Ongoing PhD Student

Mr. Sonu Bose.