Dr. Natesan Srinivasan

Personal Webpage

List of Publications

65. A. Majumdar, S. Natesan, Second-Order Uniformly Convergent Richardson Extrapolation Method for Singularly Perturbed DEgenerate Parabolic PDEs, International Journal of Applied and Computational Mathematics, (In Press).

64. N. Balasubramani, M. Guru Prem Prasad, S. Natesan, Rational Cubic Fractal Spline for Visualization of Shaped Data, Neural, Parallel and Scientific Computations, (In Press).

63. A. Das, S. Natesan, Second-order uniformly convergent numerical method for singularly perturbed delay parabolic partial differential equations,  International Journal of Computer Mathematics (In Press).

62. A. Majumdar, S. Natesan,  Alternating Direction Numerical Scheme for Singularly Perturbed 2D Degenerate Parabolic Convection-Diffusion Problems, Applied Mathematics and Computation, 313, 453 - 473, 2017.

61. S. Gowrisankar, S. Natesan, ε-Uniformly Convergent Numerical Scheme for Singularly Perturbed Delay Parabolic Partial Differential Equations, International Journal of Computer Mathematics, 94 (5), 902-921, 2017.

60. A. Das, S. Natesan, Uniformly Convergent Hybrid Numerical Scheme for Singularly Perturbed Delay Parabolic Convection-Diffusion Problems on Shishkin Mesh, Applied Mathematics and Computation, 271, 168 - 186, 2015.

59. P. Das, S. Natesan, Adaptive Mesh Generation for Singularly Perturbed Fourth-Order Ordinary Differential Equations, International Journal of Computer Mathematics, 92(3), 562 - 578, 2015.  (MR 3298069)

58. P. Das, S. Natesan, Optimal Error Estimate using Mesh Equidistribution Technique for Singularly Perturbed System of Reaction-Diffusion Boundary-Value Problems, Applied Mathematics and Computation, 249, 265 - 277, 2014. (MR 3279420)

57. S. Gowrisankar, S. Natesan, A Robust Numerical Scheme for Singularly Perturbed Delay Parabolic Initial-Boundary-Value Problems on Equidistributed Grids, Electronic Transactions on Numerical Analysis, 41, 376 - 395, 2014. (MR 3284414)

56. K. Mukherjee, 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. (MR 3267359)

55. S. Gowrisankar, S. Natesan, Uniformly Convergent Numerical Method for Singularly Perturbed Parabolic Initial-Boundary-Value Problems with Equidistributed Grids, International Journal of Computer Mathematics, 91(3), 553-577, 2014. (MR 3217588)

54.  S. Gowrisankar, S. Natesan, Robust Numerical Scheme for Singularly Perturbed Convection-Diffusion Parabolic Initial-Boundary-Value Problems on Equidistributed Grids, Computer Physics Communications, 185, 2008 - 2019, 2014. (MR 3209560)

53. P. Das, S. Natesan, Numerical Solution of a System of Singularly Perturbed Convection-Diffusion Boundary-Value Problems Using Mesh Equidistribution Technique,  Australian Journal of Mathematical Analysis and Applications,  10 (1), Art. 14, 17 pp, 2013. (MR 3128837)

52. K. Mukherjee, 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. (MR 3150013)

51. S. Gowrisankar, S. Natesan, Parameter Uniform Numerical Method for Singularly Perturbed Parabolic Reaction-Diffusion Problems on Equidistributed Grids, Applied Mathematics Letters,  26 (11), 1053-1060, 2013. (MR 3089564)

50. P. Das, S. Natesan, Richardson Extrapolation Method for Singularly Perturbed Convection-Diffusion Problems on Adaptively Generated Mesh, CMES: Computer Modeling in Engineering & Sciences, 90(6), 463-485, 2013. (MR 3099246)

49.  P. Das, S. Natesan, A Uniformly Convergent Hybrid Scheme for Singularly Perturbed System of Reaction-Diffusion Robin-Type Boundary-Value Problems, Journal of Applied Mathematics and Computing,41(1-2), 447-471, 2013. (MR 3017131)

48. S. Natesan, S. Gowrisankar, Robust Numerical Scheme for Singularly Perturbed Parabolic Initial-Boundary-Value Problems on Equidistributed Mesh, CMES: Computer Modeling in Engineering & Sciences, 88 (4), 245-268, 2012. (MR 3059044)

47. P. Das, S. Natesan, Higher-Order Uniform-Convergent Schemes for Robin-Type Reaction-Diffusion Problems Using Adaptively Generated Grid, International Journal of Computational Methods, 9(4), 2012. (MR 3016139)

46. J. Mohapatra, S. Natesan, Uniformly Convergent Numerical Method for Singularly Perturbed Differential--Difference Equation Using Grid Equidistribution,  International Journal for Numerical Methods in Biomedical Engineering, 27(9), 1427-1445, 2011. (MR 2837206)

45. J. Mohapatra, S. Natesan, Parameter-Uniform Numerical Methods for Singularly Perturbed Mixed Boundary-Value Problems Using Grid Equidistribution, Journal of Applied Mathematics and Computing, 37(1), 247- 265, 2011. (MR 2831536)

44. K. Mukherjee, S. Natesan, ε-Uniform Error Estimate of Hybrid Numerical Scheme for Singularly Perturbed Parabolic Problems with Interior Layers, Numerical Algorithms, 58(1), 103-141, 2011. (MR 2831159)

43. K. Mukherjee, 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. (MR 2806532)

42. K. Mukherjee, S. Natesan, Richardson Extrapolation Technique for Singularly Perturbed Parabolic Convection-Diffusion Problems, Computing, 92, 1-32, 2011. (MR 2794924)

41. J. Mohapatra, S. Natesan, The Parameter-Robust Numerical Method Based on Defect Correction Technique for Singularly Perturbed Delay Differential Equations with Layer Behavior, International Journal of Computational Methods, 7 (4), 573-594, 2010. (MR 2756267)

40. J. Mohapatra, S. Natesan, Parameter-uniform numerical method for global solution and global normalized flux of singularly perturbed boundary-value problems using grid equidistribution, Computers & Mathematics with Applications, 60, 1924-1939, 2010. (MR 2719712)

39. H. Ramos, J. Vigo-Aguiar, S. Natesan, R. Garcia-Rubio, M.A. Queiruga, Numerical Solution of Nonlinear Singularly Perturbed Problems on Nonuniform meshes by using a Non-Standard Algorithm, Journal of Mathematical Chemistry, 48(1), 38-54, 2010. (MR 2657913)

38. J. Mohapatra, S. Natesan, Uniform Convergence Analysis of Finite Difference Scheme for Singularly Perturbed Delay Differential Equation on an Adaptively Generated Grid, Numerical Mathematics: Theory, Methods and Applications, 3 (1), 1-22, 2010. (MR 2681554 )

37. C. Clavero, R.K. Bawa, S. Natesan, A Robust Second-Order Numerical Method for Global Solution and Global Normalized Flux of Singularly Perturbed Self-Adjoint Boundary-Value Problems, International Journal of Computer Mathematics, 86 (10-11), 1731-1745, 2009. (MR 2573169)

36. R. Deb, S. Natesan, Higher-Order Time Accurate Numerical Methods for Singularly Perturbed Parabolic Partial Differential Equations, International Journal of Computer Mathematics, 86(7), 1204-1214, 2009.  (MR 2537921)

35. K. Mukherjee, S. Natesan, Parameter-Uniform Hybrid Numerical Scheme for Time-Dependent Convection-Dominated Initial-Boundary-Value Problems, Computing,  84 (3-4), 209-230, 2009.  (MR2506261)

34. R.K. Bawa, S. Natesan, An Efficient Hybrid Numerical Scheme for Convection- Dominated Boundary-Value Problems, International Journal of Computer Mathematics, 86 (2), 261-273, 2009. (MR2488027)

33. B.S. Deb, S. Natesan, Richardson Extrapolation Method for Singularly Perturbed Coupled System of Convection-Diffusion Boundary-Value Problems, CMES: Computer Modeling in Engineering & Sciences, 38(2), 179-200, 2008. (MR2502155)

32. S. Natesan, R. Deb, A Robust Numerical Scheme for Singularly Perturbed Parabolic Reaction-Diffusion Problems, Neural, Parallel and Scientific Computations, 16, 419-434, 2008. (MR2768416)

31. K. Mukherjee, S. Natesan, An Efficient Numerical Scheme for Singularly Perturbed Parabolic Problems with Interior Layers, Neural, Parallel and Scientific Computations, 16, 405-418, 2008. (MR2768415)

30. J. Mohapatra, S. Natesan, Uniformly Convergent Second-Order Method for Singularly Perturbed Delay Differential Equations, Neural, Parallel and Scientific Computations, 16, 353-370, 2008. (MR2768412)

29. S. Natesan, R.K. Bawa, Second-order Numerical Scheme For Singularly Perturbed Reaction-Diffusion Robin Problems, Journal of Numerical Analysis, Industrial and Applied Mathematics, 2(3-4), 177-192, 2007. (MR2376088)

28. S. Natesan, B.S. Deb, A Robust Computational Method for Singularly Perturbed Coupled System of Reaction-Diffusion Boundary-Value Problems, Applied Mathematics and Computation, 188 (1), 353-364, 2007. (MR2327123)

27. S. Natesan, R.K. Bawa, C. Clavero, Uniformly Convergent Compact Numerical Scheme for the Normalized Flux of Singularly Perturbed Reaction-Diffusion Problems, International Journal of Information and Systems Sciences, 3(2), 207-221, 2007. (MR2297048)

26. R.K. Bawa, and S. Natesan, Parallel Implementation of a Spline Based Computational Approach for Singular Perturbation Problems, Lecture Notes in Computer Science, 4297, 254-262, 2006. 

25. V. Shanthi, N. Ramanujam, S. Natesan, Fitted Mesh Method for Singularly Perturbed Reaction-Convection-Diffusion Problems with Boundary and Interior Layers, Journal of Applied Mathematics & Computing, 22 (1-2), 49-65, 2006. (MR2248360)

24. S. Natesan, R.K. Bawa, C. Clavero, An ε-Uniform Hybrid Scheme for Singularly Perturbed 1-D Reaction-Diffusion Problems, Numerical Mathematics and Advanced Applications, 1079-1087, Springer, Berlin, 2006. (MR2303740)

23. J. Vigo-Aguiar,  S. Natesan, An Efficient Numerical Method for Singular Perturbation Problems, Journal of Computational and Applied Mathematics, 192, 132-141, 2006. (MR2226996)

22. C. Conca, S. Natesan, M. Vanninathan, Numerical Experiments with Bloch-Floquet Approach in Homogenization, International Journal for Numerical Methods in Engineering, 65 (9),  1444-1471, 2006. (MR2199541 2006h:35010)

21. R.K. Bawa,  S. Natesan, A Computational Method for Self-adjoint Singular Perturbation Problems Using Quintic Spline, Computers & Mathematics with Applications, 50(8-9), 1371-1382, 2005. (MR 2175596) 

20. R.K. Bawa,  S. Natesan, Uniformly Convergent Computational Technique for Singularly Perturbed Self-adjoint Mixed Boundary Value Problems, Lecture Notes in Computer Science, 3516, 1104-1107, 2005.

19. F. Duarte, R. Gormaz. S. Natesan, Arbitrary Lagrangian-Eulerian method for Navier-Stokes equations with moving boundaries, Computer Methods in Applied Mechanics and Engineering, 193 (45-47), 4819-4836, 2004. (MR 2097758)

18. J. Vigo-Aguiar,  S. Natesan, A Parallel Boundary Value Technique for Singularly Perturbed Two-Point Boundary Value Problems, The Journal of Supercomputing, 27 (2), 195-206, 2004. 

17. S. Natesan, J. Jayakumar, J. Vigo-Aguiar, Parameter Uniform  Numerical Method for Singularly Perturbed Turning Point Problems  Exhibiting Boundary Layers, Journal of Computational and Applied Mathematics, 158, 121-134, 2003. MR2013610 (2004j:65096)

16. C. Conca, S. Natesan, Numerical Methods for Elliptic Partial Differential Equations with Rapidly Oscillating Coefficients, Computer Methods in Applied Mechanics and Engineering, 192(1-2), 47-76, 2003.(MR 1951405)

15. S. Natesan, J. Vigo-Aguiar, N. Ramanujam, A Numerical Algorithm for Singular Perturbation Problems Exhibiting Weak Boundary Layers, Computers & Mathematics with Applications,  45, 469-479, 2003.(MR 1991382)

14. S. Natesan, N. Ramanujam, 'Shooting Method' for the Solution of Singularly Perturbed Two-Point Boundary-Value Problems Having Less Severe Boundary Layers, Applied Mathematics and Computation, 133(2-3), 623-641, 2002. (MR 1924642 2003f:65138)

13. S. Natesan, N. Ramanujam, An Asymptotic-Numerical Method for Singularly Perturbed Robin Problems - I, Applied Mathematics and Computation, 126(1), 97-107, 2002. (MR 1868149 2002j:34090)

12. S. Natesan, "Booster Method" for Singularly Perturbed Robin Problems - II, International Journal of Computer Mathematics, 78(1), 141-152, 2001. (MR 1893863 2003c:65059)

11. J. Vigo-Aguiar, L.M. Quintales, S. Natesan, An Efficient Parallel Algorithm for the Numerical Solution of Schrödinger Equation, Lecture Notes in Computer Science, 1981, 262-270, 2001. (MR 1907282 2003e:65187)

10. S. Natesan, N. Ramanujam, "Booster Method" for Singularly Perturbed Robin Problems-I, International Journal of Computer Mathematics,76(2), 191-202, 2000.(MR 1813315 2001k:65121)

9. S. Natesan, N. Ramanujam, A "Booster Method" for Singularly Perturbed One-Dimensional Reaction-Diffusion Neumann Problems, Journal of Optimization Theory and Applications,104(1), 175-194, 2000. (MR 1741396 2001c:65090)

8. S. Natesan, N. Ramanujam, 'Shooting Method' for Singularly Perturbed One-Dimensional Reaction-Diffusion Neumann Problems, International Journal of Computer Mathematics,72(3), 383-393, 1999. (MR 1734789)

7. S. Natesan, N. Ramanujam, A "Booster Method" for Singular Perturbation Problems Arising in Chemical Reactor  Theory by Incorporation of Asymptotic Approximations, Applied Mathematics and Computation, 100(1), 27-48, 1999. (MR 1665904 99i:65078)

6. S. Natesan, N. Ramanujam, Improvement of Numerical Solution of Self-Adjoint Singular Perturbation Problems by Incorporation of Asymptotic Approximations, Applied Mathematics and Computation, 98(2-3), 119-137, 1999. (MR 1659904 2000f:65067)

5. S. Natesan, N. Ramanujam, Booster Method for Singularly Perturbed One-Dimensional Convection -Diffusion Neumann Problems, Journal of Optimization Theory and Applications,99(1), 53-72, 1998.(MR 1653245 99j:65128)

4. S. Natesan, N. Ramanujam, Initial-Value Technique for Singularly Perturbed Turning Point Problems Exhibiting Twin Boundary Layers, Journal of Optimization Theory and Applications, 99(1), 37-52, 1998. (MR 1653241 99h:34022)

3. S. Natesan, N. Ramanujam, 'Shooting Method' for Singular Perturbation Problems Arising in Chemical Reactor Theory, International Journal of Computer Mathematics,70(2), 251-262, 1998. (MR 1712497)

2. S. Natesan, N. Ramanujam, A Computational Method for Solving Singularly Perturbed Turning Point Problems Exhibiting  Twin Boundary Layers, Applied Mathematics and Computation, 93(2-3), 259-275, 1998. (MR 1629390 99c:65146)

1. S. Natesan, N. Ramanujam, Initial-Value Technique for Singularly Perturbed Boundary-Value Problems for Second Order Ordinary Differential Equations Arising in Chemical Reactor Theory, Journal of Optimization Theory and Applications, 97(2),  455-470, 1998. (MR 1625108 99a:34038)

 

Book Chapters 

1. S. Natesan, Numerical Methods for Differential Equations,  pp. 173-213, Applied Mathematics, Editors: U. Basu, B.N. Mandal, Narosa Publishing House, New Delhi, 2008. 

2. S. Natesan, Efficient Numerical Methods for Singularly Perturbed Differential Equations, pp. 329-355, Mathematical Modeling with Multidisciplinary Applications, Editor: X-S. Yang, John Wiley & Sons, Inc., New Jersey, 2013.

 

International Conferences 
 

1. S. Natesan, J. Vigo-Aguiar, A Parallel Boundary-Value Technique for Singularly Perturbed Two-Point Boundary-Value Problems, pp. 29-35, Proceedings of the 2000 International Conference on Parallel and Distributed Processing Technology and Applications, Las Vegas, USA, Editor: H. Arabina, CSREA Press, Athens, GA, 2000.

2. J. Vigo-Aguiar, M.L. Quintales, S. Natesan, An Efficient Parallel Algorithm for the Numerical Solution of Schrödinger Equation, pp. 231-239, VECPAR 2000, Proceedings of the IV-International Meeting on Vector and Parallel Processing, University of Porto, Portugal.

3. First Latin American Congress of Mathematicians, Institute of Pure and Applied Mathematics (IMPA), Rio de Janeiro, Brazil, July 31 - August 4, 2000.

4. C. Conca, S. Natesan, M. Vanninathan, Numerical Solution of Elliptic Partial Differential Equations by Bloch Waves Method, pp. 63-83, Proceedings of the XVII CEDYA: Congress on DifferentialEquations and Applications/VII Congress on Applied Mathematics, University of Salamanca,  Salamanca, Spain, 2001. (MR 1873642 2002k:65215)

5. C. Conca, S. Natesan, M. Vanninathan, Numerical Solution of Elliptic Partial Differential Equations with rapidly oscillating coefficients by Bloch Wave Method, Proceedings of the II International Conference on Theoretical, Applied, Computational and Experimental Mechanics, Indian Institute of Technology, Kharagpur, 2001.

6. S. Natesan, J. Jayakumar, J. Vigo-Aguiar, Uniformly Convergent  Numerical Method for Singularly Perturbed Turning Point Problems, International Conference on Computational and Mathematical Methods  in Science and Engineering (CMMSE 2002), Alicante, Spain, 2002.

7. S. Natesan, J.L. Gracia, C. Clavero, Singularly Perturbed Boundary-Value Problems with Two Small Parameters - A Defect Correction Approach, pp. 1-6, Proceedings of the International Conference on Boundary and Interior Layers - Computational & Asymptotic Methods (BAIL 2004), ONERA - Centre de Toulouse, France.

8. S. Natesan, R.K. Bawa, A Parallel Computational Methods for Self-Adjoint Singular Perturbation Problems, pp. 220-226, Proceedings of Asia Pacific Conference ObComAPC-2004, Parallel and Distributed Computing Technologies, Vellore Institute of Technology, Vellore, 2004. 

9. S. Natesan, Numerical Solution of Multi-Scale Elliptic Problems  by Bloch-Floquet Approach, International Conference on Number Theory and Fourier Techniques (ICNFT'04), Srinivasa Ramanujan Centre, Sastra Deemed University, Kumbakonam, December 21-22, 2004. 

10. R.K. Bawa, S. Natesan, Quintic Spline Based Computational Scheme for Singularly Perturbed Convection-Diffusion Problems, pp. 24-28, IEEE Proceedings of the 19th  International Symposium on High Performance Computing Systems and Applications (HPSC'05), University of Guelph, Ontario, Canada, 2005. 

11. S. Natesan, R.K. Bawa, C. Clavero, An ε-Uniform Hybrid Scheme for Singularly Perturbed Reaction-Diffusion Problems, The Sixth European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2005), University of Santiago de Compostela, Spain, 2005. 

12. S. Natesan, R.K. Bawa, Second-Order Numerical Scheme for Singularly Perturbed Reaction-Diffusion Robin Problems, South African Society for Numerical and Applied Mathematics (SANUM 2006), University of Stellenbosch, South Africa, April 3 - 5, 2006. 

13. R.K. Bawa, S. Natesan, Second-Order ε-Uniformly Convergent Scheme for Singularly Perturbed Convection-Diffusion Problems, pp. 42-51, Proceedings of the International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2007, Chicago, 20 - 23 June 2007. 

14. S. Natesan, R. Deb, Efficient Numerical Schemes for Singularly Perturbed Parabolic Initial-Boundary-Value Problems, 6th International Congress on Industrial and Applied Mathematics (ICIAM 2007), Zurich, Switzerland, 16-20 July 2007. 

15. C. Clavero, R.K. Bawa, S. Natesan, An almost second-order uniform convergent computational technique for global solution and global normalized flux of singularly  perturbed reaction-diffusion problems, Proceedings of the International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2008, Murcia, Spain, 13 - 17 June 2008. 

16. S. Natesan, A second-order robust numerical method for system of singularly perturbed boundary-value problems, General Linear Methods Auckland Conference on Numerical Ordinary Differential Equations (GLADE 2008), University of Auckland, New Zealand, 14 - 18, July 2008. 

17. S. Natesan, Second-order uniformly convergent hybrid numerical scheme for singularly perturbed problems of mixed parabolic-elliptic type, International Conference on Scientific Computation and Differential Equations (Sci-CADE 2011), University of Toronto, Toronto, Canada, 11-15, July 2011.

18. S. Natesan, S. Gowrisankar, Robust numerical scheme for singularly perturbed parabolic initial-boundary-value problems, International Congress on Industrial and Applied Mathematics, (ICIAM 2011), Vancouver, Canada, 18-22, July 2011.

19.  S. Natesan, S. Gowrisankar,  Robust computational method for singularly perturbed parabolic initial-boundary-value problems on adaptive grid, European Numerical Mathematics and Advanced Applications (ENUMATH 2011), University of Leicester, Leicester, UK, 5-9, September 2011.


 

 

See the following websites for most of my publications:

  1. AMS MathSciNet website           
     
  2. ACM Digital Library Citations           
     
  3. Zentralblatt MATH                

 

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    5.    DBLP Computer Science Bibliography

 

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    8.   Researchgate    

 

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