Dr. P. P. Chakravarthy >>Publications

Research Publications (International journals):  

Total No. of publications international Journals (peer reviewed)  : 32

  1. Y. N. Reddy and P. Pramod Chakravarthy: Method of Reduction of Order for Solving Singularly Perturbed Two-Point Boundary Value Problems, Applied Mathematics and Computation, Vol. 136(2003), pp. 27-45. (Elsevier, SCI)
  2. Y. N. Reddy and P. Pramod Chakravarthy: Numerical Patching Method for Singularly Perturbed Two-Point Boundary Value Problems Using Cubic Splines, Applied Mathematics and Computation, Vol. 149 (2004), pp.441-468.  (Elsevier, SCI)
  3. Y. N. Reddy and P. Pramod Chakravarthy: An Exponentially Fitted Finite Difference Method for Singular Perturbation Problems, Applied Mathematics and Computation, Vol. 154 (2004), pp.83-101. (Elsevier, SCI)
  4.  Y. N. Reddy  and P. Pramod Chakravarthy:  An Initial-Value Approach for Solving Singularly Perturbed Two-Point Boundary Value Problems, Applied Mathematics and Computation, Vol. 155(2004), pp.95-110.(Elsevier, SCI)
  5.   P. Pramod Chakravarthy and  Y. N. Reddy: An Exponentially Fitted Modified Upwind Scheme for Singular Perturbation Problem, International Journal of Fluid Mechanics Research, Vol.33, issue 2 (2006), pp 119-136.(Begell House, Inc., USA., Scopus)
  6. P. Pramod Chakravarthy, K. Phaneendra and Y. N. Reddy: A Seventh order Numerical Method for Singular Perturbation Problems, Applied Mathematics and Computation, Vol. 186 (2007), pp 860-871.(Elsevier, SCI) 
  7.  P. Pramod Chakravarthy and Y. N. Reddy:  A cutting point technique for Singular Perturbation Problems, Journal of Mathematical Control Science and Applications, Vol. 1, No. 1(2007), pp 39-59.   
  8. P. Pramod Chakravarthy and Y. N. Reddy: A Pair of Independent Initial Value Problems for Singularly Perturbed Two-Point Boundary Value Problems, International Journal of Scientific Computing, Vol. 1, No. 2 (2007), pp 123 – 143. 
  9. P. Pramod Chakravarthy, K. Phaneendra and Y. N. Reddy: A Fifth Order Numerical Method for Singular Perturbation Problems, J. Appl. Math. & Informatics Vol. 26(2008), No. 3 – 4, pp. 689 –706. (Korean SIGCAM and KSCAM)
  10. P. Pramod Chakravarthy, K. Phaneendra and Y. N. Reddy:  A Fifth order Numerical Method for Singularly Perturbed differential-difference equations with negative shift, J. Appl. Math. & Informatics, Vol. 27(2009), No. 1 – 2, pp 441 – 452.   (Korean SIGCAM and KSCAM)
  11. Bhagwat Thakran, A.G. Deshpande and P. Pramod Chakravarthy:  A Numerical Method for Solving Singularly Perturbed two point Boundary Value Problems using Rational Approximation, International Journal of Computational Intelligence Research & Applications, Vol. 3, No. 2 (2009), pp 185 – 192. 
  12. K. Phaneendra, P. Pramod Chakravarthy and Y. N. Reddy:  A Fitted Numerov Method for Singular Perturbation Problems Exhibiting Twin Layers, Applied Mathematics & Information Sciences   … An    international journal, Vol. 4, Number 3, (2010), PP 341–352.   1) (Dixie W Publishing Corporation,U.S.A., SCI)
  13. P. Pramod Chakravarthy and A.G. Deshpande:  Numerical Solution of Singular Perturbation Problems by Asymptotic Boundary Condition, Int. J. of Appl. Math and Mech. Vol. 7, No. 4(2011), 70-96.(Indexed in the Zentralblatt database)
  14. R. Nageshwar Rao, P. Pramod Chakravarthy: A Fourth order finite difference method for singularly perturbed differential difference equations, American Journal of Computational and Applied Mathematics, 1 (1): 5-10 (2011), DOI: 10.5923/j.ajcam.20110101.02
  15. P. Padmaja, P. Pramod Chakravarthy, Y.N. Reddy:  A Non Standard Explicit Method for Solving Singularly Perturbed Two point Boundary Value Problems via Method of Reduction of Order, Int. J. of Appl. Math. and Mech. 8(2): 62-76, 2012.(Indexed in the Zentralblatt database)
  16. R. Nageshwar Rao, P. Pramod Chakravarthy:  Numerical Patching Technique for Singularly Perturbed Nonlinear Differential-Difference Equations with a negative shift, Applied Mathematics 2012, 2(2): 11-20 DOI: 10.5923/j.am.20120202.04
  17. P. Pramod Chakravarthy, R. Nageshwar Rao:  A domain decomposition method for Singularly Perturbed Differential-Differential Equations with a small negative shift, European journal of scientific research, Vol.75 No.2 (2012), pp. 193-215.(SCI)
  18. P. Padmaja, P. Pramod Chakravarthy, Y.N. Reddy: An Asymptotic Method for Singularly Perturbed Two-Point boundary Value Problems via Initial Value approach, European journal of scientific research, Vol.82 No.3 (2012), pp.340-353.(SCI)
  19.  P. Pramod Chakravarthy, R. Nageshwar Rao:  A Modified Numerov Method for solving Singularly Perturbed Differential-Difference Equations arising in Engineering and Science, Results in Physics 2 (2012) 100–103.(Elsevier, SCI)
  20. P. Padmaja , P. Pramod Chakravarthy , Y. N. Reddy: A Numerical Scheme for Nonlinear Singularly Perturbed Two point Boundary Value Problems using Locally Exact Integration, American Journal of Computational and Applied Mathematics , Vol. 2, No. 6 (2012), pp. 306-310. doi: 10.5923/j.ajcam.20120206.09.
  21. P. Pramod Chakravarthy, R. Nageshwar Rao:  A Finite Difference Method for Singularly Perturbed Differential-Difference Equations with Layer and Oscillatory Behavior, Applied Mathematical Modelling,  37 (2013), pp. 5743-5755, DOI: 10.1016/j.apm.2012.11.004.(Elsevier, SCI)
  22. P. Pramod Chakravarthy, R. Nageshwar Rao:  An initial value technique for singularly perturbed differential-difference equations with a small negative shift, J. Appl. Math. & Informatics Vol. 31(2013), No. 1 – 2, pp. 131 – 145.(Korean SIGCAM and KSCAM)
  23. R. Nageshwar Rao, P. Pramod Chakravarthy: A finite difference method for singularly perturbed differential-difference equations arising from a model of neuronal variability, Journal of Taibah University for Science 7 (2013) 128–136.(Elsevier)
  24. R. Nageshwar Rao, P. Pramod Chakravarthy: A fitted Numerov method for singularly perturbed parabolic partial differential equation with a small negative shift arising in control theory, Numerical Mathematics: Theory, Methods and Applications, Vol. 7 (2014), No. 1, pp. 23-40.(Cambridge university Press, SCI)
  25. R. Nageshwar Rao, P. Pramod Chakravarthy: An Exponentially Fitted Tridiagonal Finite Difference Method for Singularly Perturbed Differential-Difference Equations with Small Shift, Ain Shams Engineering Journal, (2014) 5, 1351–1360.Elsevier, Scopus)
  26.  Podila Pramod Chakravarthy, S Dinesh Kumar, Ragi Nageshwar Rao and Devendra P Ghate : A fitted numerical scheme for second order singularly perturbed delay differential equations via cubic spline in compression, Advances in Difference Equations 2015, 2015:300  doi:10.1186/s13662-015-0637-x, http://www.advancesindifferenceequations.com/content/2015/1/300.(Springer, SCI)
  27. P. Pramod Chakravarthy,  S. Dinesh Kumar, R. Nageshwar Rao:  An exponentially fitted finite difference scheme for singularly perturbed delay differential equations with large delays, Ain Shams Engineering Journal,  Ain Shams Engineering Journal (2017) 8, 663–671.(Elsevier, Scopus)
  28. P. Pramod Chakravarthy, S. Dinesh Kumar, R. Nageshwar Rao: Numerical Solution of Second Order Singularly Perturbed Delay Differential Equations via Cubic Spline in Tension, International Journal of Applied and Computational Mathematics, September 2017, Volume 3, Issue 3, pp 1703–1717. DOI 10.1007/s40819-016-0204-5.(Springer)
  29. R. Nageshwar Rao, P. Pramod Chakravarthy,  “Fitted numerical methods for singularly perturbed one-dimensional parabolic partial differential equations with small shifts arising in the modelling of neuronal variability", Differ Equ Dyn Syst, DOI 10.1007/s12591-017-0363-9.(Springer, Scopus)
  30. P. Pramod Chakravarthy,  S. Dinesh Kumar, R. Nageshwar Rao:  An Exponentially Fitted Spline Method for Second Order Singularly Perturbed Delay Differential Equations, Iran J Sci Technol Trans Sci, DOI 10.1007/s40995-017-0253-6. (Springer SCI).
  31. P. Pramod Chakravarthy,  Kamlesh Jangir, A novel method for singularly perturbed delay differential equations of reaction diffusion type, Differential equations and dynamical systems , DOI 10.1007/s12591-017-0399-x.(Springer, Scopus)
  32. S Dinesh Kumar , R Nageshwar Rao and P Pramod Chakravarthy: A numerical scheme for singularly perturbed reaction-diffusion problems with a negative shift via Numerov method, IOP Conf. Series: Materials Science and Engineering 263 (2017) 042110, doi:10.1088/1757-899X/263/4/042110. (Scopus)  

 

Research Publications in International Conferences (Conducted in India):     02

1. P. Pramod Chakravarthy and Y. N. Reddy: A Fourth Order Fitted Numerical Scheme for Singular Perturbation Problems, Proceedings of Indian Society of Theoretical and Applied Mechanics (ISTAM), conducted by IIT Kharagpur (2005), pp 142-154.

2. K. Phaneendra, P. Pramod Chakravarthy and Y. N. Reddy:  Method of Reduction for Singularly Perturbed Boundary Value Problems with mixed boundary conditions, proceedings of International Conference on ‘Challenges and Applications of Mathematics in Science and Technology’, conducted by NIT Rourkela (2010), pp 775 – 784. ( ISBN 023 – 032 – 875 – X, published by Macmillan Advanced research series).