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

• Finite Difference and Finite Element methods for Singularly Perturbed Problems
• Numerical Techniques for Parabolic PDEs
• Multi-Scale Problems

Awards

• Awarded Post-doctoral Fellowship by National Board of Higher Mathematics (NBHM), DAE, Govt. of India, 2010.
• Qualified National Eligibility Test (NET) for Lectureship in Mathematical Sciences, conducted by CSIR, New Delhi, India, 2005.
• Qualified Graduate Aptitude Test in Engineering (GATE), MHRD, Govt. of India, 2004.
• Awarded 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.

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, 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 in Referred Conferences / Training Programme:

1. Delivered a talk in “YOUNG TALENT NURTURE-2014” program, held at Department of Mathematics, Indian Institute of Space Science and Technology (IIST), Thiruvananthapuram, from 13th May to 25th May, 2014, for the 2nd year B.Sc, B.Tech and integrated M.Sc students with Mathematics as one of their subjects of study.
2. Delivered a talk on “Uniformly convergent numerical method for 2D Singularly Perturbed Problems”, in the International Conference on Emerging Trends in Applied Mathematics, held at Department of Mathematics, University of Calcutta, February 12-14, 2014.
3. Delivered a talk in “YOUNG TALENT NURTURE-2013” program, held at Department of Mathematics, Indian Institute of Space Science and Technology (IIST), Thiruvananthapuram, from 28th May to 8th June, 2013, for the 1st year B.Sc, B.Tech and integrated M.Sc students with Mathematics as one of their subjects of study.
4. Delivered a talk on “Efficient Numerical Scheme for 2D Singularly Perturbed Parabolic Convection-Diffusion Problems”, in the National Conference on Analysis and Differential Equations (NCFADE-2012), held at Department of Mathematics, Bharathidasan University, Tiruchirappalli, December 19-20, 2012.
5. Delivered a talk on “Hybrid numerical scheme for singularly perturbed problems of mixed parabolic-elliptic type”, in the 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.
6. Delivered a talk on “A unified approach for uniform convergence of upwind scheme on Shishkin type meshes for singularly perturbed parabolic problems”, in the 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.
7. Delivered a talk on “Uniformly Convergent Hybrid Scheme for Singularly Perturbed Parabolic Problems with Discontinuous Convection Coefficient”, in the International Conference on Recent Trends in Computational PDEs (ICCPDE-08), held at Department of Mathematics, Indian Institute of Technology, Bombay, December 10-13, 2008.
8. Delivered a talk on “An Efficient Numerical Method for Singularly Perturbed Parabolic Initial-Boundary-Value Problems”, in the 52nd congress of Indian Society of Theoretical and Applied Mechanics (ISTAM), held at B.N.M. Institute of Technology, Bangalore, December 14-17, 2007.

Participated 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.
3. International Workshop on “Recent Trends in Computational Partial Differential Equations” (ICCPDE-08), held at Department of Mathematics, IIT Bombay during December 7-13, 2008.

•     Awarded Post-doctoral Fellowship by National Board of Higher Mathematics (NBHM), DAE, Govt. of India, 2010.
•     Qualified National Eligibility Test (NET) for Lectureship in Mathematical Sciences, conducted by CSIR, New Delhi, India, 2005.
•     Qualified Graduate Aptitude Test in Engineering (GATE), MHRD, Govt. of India, 2004.
•     Awarded 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.

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