Numerical Analysis, Numeric’s of Delay Differential Equations, Fractional Differential Equations Numerical Methods with analysis for Singular Boundary Value Problems and Singular Perturbation Problems
1. Design and analysis of a computational procedure for a class of time fractional multi-term diffusion problem, Soft Computing, (with Deepika) (Accepted)
2. Natural transform decomposition method for the numerical treatment of the time fractional Burgers–Huxley equation, Numerical Methods for Partial Differential Equations. (with K. Aruna and K. Raghavendar) (Accepted)
3. A Novel Three-step Iterative Approach for Oscillatory Chemical Reactions of Fractional Brusselator Model, International Journal of Modelling and Simulation. (with Sangeeta Devi) (Accepted)
4. Numerical solutions of nonlinear time fractional Klein-Gordon equation via natural transform decomposition method and iterative Shehu transform method, Journal of Ocean Engineering and Science (with Aruna, Raghavendar, H Rezazadeh, M Inc) (Accepted)
5. A computational approach for numerical simulations of the fractal–fractional autoimmune disease model, Chaos, Solitons & Fractals, 165 (2) (2022) 112829. (with Sangeeta)
6. A computational procedure and analysis for multi‐term time‐fractional Burgers‐type equation, Mathematical Methods in the Applied Sciences, 45(16) (2022) 9218 – 9232. (with Neetu Garg)
7. Numerical solutions of time fractional Sawada Kotera Ito equation via natural transform decomposition method with singular and nonsingular kernel derivatives, 44(18) (2022) 14025 – 14040. Mathematical Methods in the Applied Sciences (with K. Aruna and K. Raghavendar)
8. Numerical Solutions of Time Fractional Zakharov-Kuznetsov Equation via Natural Transform Decomposition Method with Nonsingular Kernel Derivatives, Journal of Function Spaces, Volume 2021, Article ID 9884027. (with MX Zhou, Aruna, Raghavendar, H Rezazadeh, M Inc)
9. Numerical treatment and analysis for a class of time-fractional Burgers equation with the Dirichlet boundary conditions, International Journal of Computational Science and Engineering, 25 (1)(2022), 74-90. (with Neetu Garg)
10. A practical numerical approach to solve a fractional Lotka-Volterra population model with non-singular and singular kernels, Chaos, Solitons & Fractals, 145 (2021), 110792. (with Sangeeta Devi) (Elsevier)
11. An unconditionally stable algorithm for multi-term time-fractional advection-diffusion equation with variable coefficients and convergence analysis, Numerical Methods for Partial Differential Equations, 37 (3) (2021), 1928-1945. (with Neetu Garg) (Wiley)
12. Numerical Simulation for a class of Singularly Perturbed Convection Delay Problems, Khayyam J. Math. 7 (2021), no. 1, 52–64. (with P Murali Mohan Kumar).
13. A Numerical Approach for Solving Nonlinear Singularly Perturbed Boundary Value Problem Arising in Control Theory, Journal of Applied Nonlinear Dynamics, 10(1), 151 – 159 (2021). (with P Murali Mohan Kumar)
14. Computational study for a class of time-dependent singularly perturbed parabolic partial differential equation through tension spline, Computational and Applied Mathematics, 39(3), (2020) 233. (with P. Murali Mohan Kumar) (Springer)
15. A numerical approach for a class of time-fractional reaction-diffusion equation through exponential B-spline method, Computational and Applied Mathematics, 39 (1) (2020), 37. (with Neetu Garg) (Springer)
16. Computational results and analysis for a class of linear and nonlinear singular perturbed convection delay problems on Shishkin mesh, Hecettepe Journal of Mathematics & Statistics. 49 (1) (2020), 221-235. (with P. Murali Mohan Kumar)
17. Oscillatory flow of an incompressible couple stress fluid generated by the rotary oscillations of two concentric spheres, AIP Conference Proceedings 2277 (2020), 030020. (with VG Vani)
18. An Implicit Numerical Scheme for a Class of Multi-term Time-Fractional Diffusion Equation, The European Physical Journal Plus, 134 (6) (2019)312. (with Neetu Garg) (Springer)
19. Solutions of strongly nonlinear oscillators via Haar wavelets, AIP Conference Proceedings 2112 (1) (2019), 020003. (with VG Vani)
20. Analytical Solutions of the Bloch Equation via Fractional Operators with Non-singular Kernels, Applied Mathematics and Scientific Computing, Trends in Mathematics, 37-45, (2019). (with Neetu Garg) (Springer)
21. Application and Analysis of Spline Approximation for Time Fractional Mobile-Immobile Advection-Dispersion Equation, Numerical Methods for Partial Differential Equations, 34(5),1799-1819(2018). (with Deepika) (Wiley)
22. Numerical Method for a Class of Nonlinear Singularly Perturbed Delay Differential Equations Using Parametric Cubic Spline, International Journal of Nonlinear Sciences and Numerical Simulation,19(3-4), 357-365(2018). (with P. Murali Mohan Kumar) (De-Gruyter)
23. Exponential Spline Method for One Dimensional Nonlinear Benjamin-Bona-Mahony-Burgers Equation, Communications in Computer and Information Science, 834, 205-215(2018). (with Deepika) (Springer)
24. Analysis and numerical simulation for a class of time fractional diffusion equation via tension spline, Numerical Algorithms 79(2), 479–497(2018). (with Deepika) (Springer)
25. Computational Simulations for Solving a Class of Fractional Models via Caputo-Fabrizio Fractional Derivative, Procedia Computer Science, 476-482 (2018). (with Neetu Garg) (Elsevier)
26. A Numerical Technique for Solving Nonlinear Singularly Perturbed Delay Differential Equations, Mathematical Modelling and Analysis, 23(1), 64-78 (2018). (with P. Murali Mohan Kumar).
27. Numerical analysis of two-parameter singularly perturbed boundary value problems via fitted splines, Analysis, 37(3), 133-143 (2017). (with P. Murali Mohan Kumar) (De-Gruyter)
28. A numerical approach for solving singularly perturbed convection delay problems via exponentially fitted spline method, Calcolo, 54(3), 943-961 (2017). (with P. Murali Mohan Kumar) (Springer)
29. Non-Polynomial Spline Method for One Dimensional Nonlinear Benjamin-Bona-Mahony-Burgers Equation, International Journal of Nonlinear Sciences and Numerical Simulation, 18(3-4), 277-284 (2017). (with Deepika) (De-Gruyter)
30. Numerical Treatment for A Singularly Perturbed Convection Delayed Dominated Diffusion Equation Via Tension Splines, International Journal of Pure and Applied Mathematics, 113(6), 110-118 (2017). (with P. Murali Mohan Kumar) (Academic Publications)
31. Solution of Nonlinear Equations Arising in Heat Transfer Through Parameterized Perturbation Method, International Journal of Pure and Applied Mathematics, 113(9), 157-165 (2017). (with K. Aruna and Geetha Vani) (Academic Publications)
32. Solution of time fractional Black-Scholes European option pricing equation arising in financial market, Nonlinear Engineering -Modeling and Application, 5(4), 269-276 (2016). (with K. Aruna) (De Gruyter)
33. Solution of fractional third-order dispersive partial differential equations, Egyptian Journal of Basic and Applied Sciences Vol. 2(3), 190-199 (2015). (with K. Aruna) (Elsevier)
34. Solution for singularly perturbed problems via cubic spline intension, Journal of Information and Computing Science, 11(4), 262-269 (2016). (with K. Aruna) (World Academic Press)
35. Two-Dimensional Differential Transform Method and Modified Differential Transform Method for Solving Nonlinear Fractional Klein–Gordon Equation, National Academy Science Letters, 37, (2), 163-171 (2014). (with K. Aruna) (Springer)
36. A Haar Wavelet Study on Convective-Radiative Fin under Continuous Motion with Temperature-Dependent Thermal Conductivity, Walailak Journal of Science and Technology, 11(3), 211-224 (2014). (with Uday Kumar)
37. Differential transform – Pade technique for treating non-linear Singular Boundary value problems arising in the Applied Sciences, International Journal of Nonlinear Sciences and Numerical Simulation, 5(2013) 247 – 254. (with K. Aruna) (De Gruyter)
38. A Computational technique for solving Singularly Perturbed Boundary Value Problems, International Journal of Applied Mathematics and Computation, 5(1)(2013)22 – 27. (Darbose Publications)
39. Approximate Solutions of Non-linear Fractional Schrodinger Equation Via Differential Transform Method and Modified Differential Transform Method, National Academy Science Letters, 36(2) (2013), 201-213. (with K. Aruna) (Springer)
40. A novel approach for a class of higher order nonlinear singular boundary value problems, International Journal of Pure and Applied Mathematics, 84(4) (2013), 321-329. (with K. Aruna) (Academic Publications)
41. Solution of singular two point boundary value problems with forcing function in integral form via differential transform method, World Journal of Mathematical Science, Vol. 9 (2013) No. 4, pp. 262-268. (with K. Aruna) (World Academic Press)
42. Application of the Haar wavelet method on continuously moving convective-radiative fin with variable thermal conductivity, Heat Transfer – Asian Research,42(4), (2013), 335-351. (with Uday Kumar) (Wiley)
43. Comparison Study of Differential Transform Method with Finite Difference Method for Magnetoconvection in a Vertical Channel, Heat Transfer – Asian Research, 42 (3) (2013), 243-258. (with J.C. Umavathi and M. Shekar) (Wiley)
44. Mixed Convective Flow in a Vertical Channel Filled with Porous Medium using Differential Transform Method, International Journal of Mathematical Archive, 4(3), (2013) 291-299. (with J.C. Umavathi and M. Shekar).
45. A Spline based computational simulations for solving self-adjoint singularly perturbed two-point boundary value problems, Journal of Information and Computing Science, 7 (4), 2012, 303-314 (with K. Aruna) (World Academic Press)
46. Comparison of two Dimensional DTM and PDTM for solving Time-Dependent Emden-Fowler Type Equations, International Journal of nonlinear Science, (World Academic Press), 13(2)(2012),228-239. (with K. Aruna)
47. He’s varational iteration method for treating non-linear singular boundary value problems, Computers &Mathematics with Application 60 (2010), 821 – 829. (with K. Aruna) (Elsevier)
48. Two-dimensional differential transform method for solving linear and non-linear Schrödinger equations, Chaos, Solitons and Fractals, 41 (2009), 2277 – 2281. (with K. Aruna) (Elsevier)
49. He’s Homotopy perturbation method for solving higher order boundary value problems, Chaos, Solitons and Fractals, 41(2009) 1905 -1909. (with K. Aruna) (Elsevier)
50. Differential transform method for solving the linear and nonlinear Klein-Gordon equation, Computer Physics Communications, 180(2009) 708 – 711. (with K. Aruna) (Elsevier)
51. Variational iteration method for twelfth-order boundary value problems, Computers & Mathematics with Application, 58(11-12)(2009) 2360-2364. (with K. Aruna) (Elsevier)
52. Differential transform method for solving linear and non-linear systems of partial differential equations, Physics Letters A, 372 (2008) 6896–6898. (with K. Auna) (Elsevier)
53. Solution of singular two-point boundary value problems using differential transformation method, Physics Letters A, 372 (2008), 4671 – 4673. (with K. Aruna)) (Elsevier)
54. A Numerical Integration Method for Singular Perturbation Problems, SAE Transactions: Journal of Passenger Cars-Mechanical Systems, (2007) Vol 116, 223 – 231. (with Y.N. Reddy and Rao. V. Dukkipati).
55. Cubic Spline polynomial for solving nonlinear singular two-point Boundary Value Problems, Applied Mathematics and Computation, 189(2) (2007) 2017–2020. (Elsevier
56. Cubic Spline for a class of singular boundary value problems arising in physiology, Applied Mathematics and Computation, 174(1) (2006) 768–774. (with Vishnu) (Elsevier)
57. Cubic Spline for a Class of Singular Two-Point Boundary Value Problems, Applied Mathematics and Computation, 170(2) (2005) 733–740. (with Y.N. Reddy) (Elsevier)
58. Higher-Order Finite Difference Method for a Class Singular Boundary Value Problems, Applied Mathematics and Computation, 155(1) (2004) 249–258. (with Y.N. Reddy) (Elsevier)
59. A Numerical Method for Singular Boundary Value Problems via Chebyshev Economizition, Applied Mathematics and Computation, 146/2–3 (2003) 691–700. (with Y.N. Reddy) (Elsevier)
60. A Numerical Method for solving two-point Boundary Value Problems over Infinite Intervals, Applied Mathematics and Computation, 144 (2003) 483–494.(with Y.N. Reddy) (Elsevier)
61. The Method of Inner Boundary Condition for Singular Boundary Value Problems, Applied Mathematics and Computation, 139/2–3 (2003), 429 – 436. (with Y.N. Reddy) (Elsevier).
1. Numerical Simulation of Time Fractional Advection-Diffusion-Reaction Equation using Exponential B-Splines, Renewable Energy Towards Smart Grid, 133-143, 2022. (with Neetu Garg)
2. Application of singular perturbation theory in modeling and control of flexible robot arm, International Journal of Advanced Technology and Engineering Exploration; 3(24) (2016): 176-181 (with Mohit Garg, and A. Swarup)
3. Numerical Solutions for Convection-Diffusion Equation through Non-Polynomial Spline. MATEC Web of Conferences. Vol. 57. EDP Sciences, 2016. (with Deepika)
4. The numerical simulation of convection delayed dominated diffusion equation. MATEC Web of Conferences. Vol. 57. EDP Sciences, 2016. (with P. Murali Mohan Kumar)
5. Modal Analysis of Composite Cantilevers in MEMS, Proceeding of International Conference on Advanced Research in Mechanical Engineering 2013, pages: 10–12 (with Bini Koshy Varghese) ISBN: 987-93-83060-03-0
6. Computational simulations for solving power-law fin-type problems via Haar wavelets, Proceedings of 56th Congress of ISTAM 2011, pages: 245 – 250.(with N. Uday Kumar)
7. He’s VarationalIterational Iteration method for solving higher order linear and nonlinear boundary value problems, Proceedings of 54th Congress of ISTAM 2009, pages: 209 – 213. (with K. Aruna)
8. Homotopy perturbation method for solving sixth-order boundary value problems, Proceedings of 53rd Congress of ISTAM 2008, pages: 267 – 276, (with B. Satyanarayana)
9. Numerical Solution of Singular Boundary Value problems by Terminal Boundary Value Technique, Proceedings of 45th Congress of ISTAM 2000, pages: 39 – 45,(with Y.N. Reddy)
i) Four Completed
ii) In Progress Two
iii) Guided Three M. Phil. Dissertations
a) Guided Two Dissertation
Sponsored R &D Projects:
a) Completed Major Research Projects
i) As a Principal Investigator to an NBHM sponsored project entitled “A Computational Approach for Singularly Perturbed Differential Difference Equations with Delay as well as Advance” Amount of Grant: 9.125 Lakhs, Period 2014-2017.
ii) As a Principal Investigator to a DRDO sponsored project entitled “Numerical Modelling and Simulation of Boundary Layer Problems i.e. Singular Singularly Perturbed Two-Point Boundary Value Problem”. Amount of Grant: 4.49 Lakhs, Period: 2011 – 2012.
iii) Co-Principal Investigator to a DRDO sponsored project entitled “Some nonlinear Hydrodynamic and Hydromagnetic fluid flows in non-uniform channels with oscillating walls” Amount of Grant: 13.96 lakhs, Period: 2004 – 2006.
iv) Co-Principal Investigator to a DRDO sponsored project entitled “Investigations of Hydromagnetic Boundary layers in rotating flows with β-plane approximation”. Amount of Grant: 14.85 lakhs, Period: 2005 – 2008.
i. Professor-in-charge (Academic) (Sep 2021 – Till Date)
ii. Head, Department of Mathematics, (July 2015 – June 2017) (from July 2019-June 2021)
iii. Professor-in-charge (Examinations), (01-08- 2017 – 31-05-2019)
iv. Professor-in-charge (Academic & Examination), (26-12- 2016- 10-08-2017)
v. Professor In-charge (Academic & Senate Affairs), (21-05-15- 25-12-2016)
vi. Chairman, Department Academic Committee, Department of Mathematics
vi. Chairman, Departmental Research Committee, Department of Mathematics
viii. Deputy Coordinator, External Peer Review, NIT-Kurukshetra
ix. Chairman, Institute Funiture Procurement Committee, NIT-Kurukshetra (2-01-2015 – till date)
x. Member, Integrated Institute Management Software Committee, NIT-Kurukshetra
xi. Member, Industry Cell, NIT-Kurukshetra
xii. Member Institute Health Centre Committee (28-3-16- till date)
xiii. Member, Campus Security Issues, NIT-Kurukshetra (17-11-2014 – till date)
xiv. Warden, Hostel No-2, (18-07-2014 to 14-09-2015)
1. Talk on ” Fractional Calculus and Some Issues” on 5 June 2021 in the 22nd virtual webinar organized by the School of Applied Science, Department of Mathematics, REVA University, Bengaluru.
2. Talk on ” Eigenvalues and Eigenvectors and application to simulation” on 30 Sep 2020 in the online faculty development program on Applied Numerical Methods by University College for Women, Koti, Hyderabad.
3. Talk on “Matrix Methods for System of Differential Equations” on 11-07- 2020 at One day National Level Webinar organized by SITAMS – IQAC, SITAMS Chittor, A. P. – 517 127
4. Talk on ” Numerical Simulation for a Class of Fractional Differential Equations” in the 11th conference on National Conference on Mathematical Techniques and Applications conducted by the Department of Mathematics, SRM Institute of Science & Technology, Kattankulathur during 11-12 Jan 2019.
5. Talk on “Time-Dependent Singularly Perturbed Parabolic Partial Differential Difference Equations” in the STTP on Mathematical Modeling & Numerical Techniques in Engineering and Science conducted by the Department of Mathematics, NIT Warangal during 9-13 Oct 2018.
6. Talk on “Numeric’s for fractional differential equations” in the International Conference on Computational Fluid Flow and Heat Transfer conducted by the Department of Mathematics, Osmania University, Hyderabad during 28-29 March 2018.
7. Talk on “Numerical simulations for treating power-law fin-type problems through Haar Wavelets” in the National Conference on “EMERGING TRENDS IN FLUID MECHANICS” conducted by Department of Mathematics, Christ University, Bengaluru during 29-30 April 2016
8. Talk on “Numerical Solutions for singularly perturbed problems via tension spline with a fitting factor” in the International Conference on Recent Advances in Mathematical Sciences and Applications (RAMS-13) conducted by Gayatri Vidya Parishad – Prof. V. Lakshmikantam Institute for Advanced Studies, Vizag during December 19 – 22, 2013.
9. Talk on “ Cubic Spline in Tension for Singularly Perturbed Problems” in the National Seminar on Recent Developments in Mathematical Sciences conducted by Sri Venkateswara University, Tirupathi on 28, June 2013.
10. Talk on “DTM for Singular Two-point Boundary Value Problems” in the National Seminar on Recent Trends in Mathematics conducted by Sri Venkateswara University, Tirupathi on 22, Dec 2012.
11. Talk on “ Comparison of Two Dimensional Differential Transform Method and Projected Differential Transform Method” in the III National Conference on Emerging Trends in Fluid Mechanics and Graph Theory conducted by Christ University, Bangalore on 16 -17, Feb 2012.
12. Talk on “Differential transform technique and its applications for initial and boundary value problems” in the National Conference on Frontiers in Fluid Mechanics conducted by Gulbarga University on 22 – 23, Feb 2011.