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B.E.(Biotechnology)
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Anil Kumar

goa Mathematics

Associate Professor

Numerical Analysis, Optimal Control Theory
Department of Mathematics, BITS Pilani K.K. Birla Goa Campus, Zuarinagar, South Goa, Goa-403726
anilpundir@goa.bits-pilani.ac.in
anilpundir@gmail.com
0832-2580446
https://www.linkedin.com/in/dr-anil-kumar-89282a9/

Published:

  • Joshi, M. C., & Kumar, A. (2005). Approximation of exact controllability problem involving parabolic differential equations. IMA Journal of Mathematical Control and Information, 22(3), 350-363. DOI: https://doi.org/10.1093/imamci/dni032
  • Kumar, A., Joshi, M. C., & Pani, A. K. (2007). On approximation theorems for controllability of non-linear parabolic problems. IMA Journal of Mathematical Control and Information, 24(1), 115-136. DOI: https://doi.org/10.1093/imamci/dnl012
  • Sonawane, R. B., Kumar, A., & Nimse, S. B. (2013). Numerical optimal control for bilinear hyperbolic PDEs. In 2013, Nirma University International Conference on Engineering (NUiCONE), IEEE. 1-5. DOI: 10.1109/NUiCONE.2013.6780203.
  • Baths, V., Singh, T., & Kumar, A. (2014). Disruption of cell wall fatty acid biosynthesis in Mycobacterium Tuberculosis using the concept of minimum robust domination energy of graph. Annual Research & Review in Biology, 4(12), 2037-2044. DOI: https://doi.org/10.9734/ARRB/2014/8960.
  • Sonawane, R. B., Kumar, A., & Nimse, S. B. (2014). Optimal control for a vibrating string with variable axial load and damping gain. IFAC Proceedings Volumes, 47(1), 75-81. (3rd International Conference on Advances in Control and Optimization of Dynamical Systems (ACDOS-2014), March 13-15, 2014, IIT Kanpur, Kanpur, India, International Federation of Automatic Control (IFAC), Elsevier). DOI:  https://doi.org/10.3182/20140313-3-IN-3024.00087)
  • Sonawane, R. B., Kumar, A., & Nimse, S. B. (2014). Exact controllability of wave equation with multiplicative controls. Applied Mathematics E-Notes, 14, 45-52. DOI: https://www.emis.de/journals/AMEN/2014/131217(final).pdf
  • Kumar, A., Pani, A. K., & Joshi, M. C. (2016). Approximate controllability of a class of partial integro-differential equations of parabolic type. arXiv preprint arXiv:1606.03673. DOI: https://arxiv.org/pdf/1606.03673.pdf
  • Sonawane, R. B., & Kumar, A. (2017). Optimal control of the velocity term in a Kirchhoff plate equation with multiplicative control.  Proceedings of International Conference on Computational Modelling and Simulation (ICCMS), 248-251, ISBN: 978-955-703011-1.
  • Kumar, P., & Kumar, A. (2017). Annuli containing all the zeros of a polynomial. Alabama Journal of Mathematics, 41, 1-6. DOI: http://www.ajmonline.org/wp-content/uploads/2018/12/final_AJM_PKAK_2017.pdf
  • Lamichhane, B. P., Kumar, A., & Kalyanaraman, B. (2017). A mixed finite element method for elliptic optimal control problems using a three-field formulation. ANZIAM Journal, 59, C97-C111. DOI: https://doi.org/10.21914/anziamj.v59i0.12643
  • Sonawane, R., & Kumar, A. (2018). Controllability of a space-time fractional order parabolic equation. hal-01948683. DOI: https://hal.archives-ouvertes.fr/hal-01948683
  • Kumar, B. S., Danumjaya, P., & Kumar, A. (2019). A fourth-order orthogonal spline collocation method to fourth-order boundary value problems. International Journal for Computational Methods in Engineering Science and Mechanics, 20(5), 460-470. DOI: https://doi.org/10.1080/15502287.2019.1600070
  • Dhayal, R., Malik, M., Abbas, S., Kumar, A., & Sakthivel, R. (2021). Approximation theorems for controllability problem governed by fractional differential equation. Evolution Equations & Control Theory, 10(2), 411. DOI: https://www.aimsciences.org/article/doi/10.3934/eect.2020073
  • Pradhan, S. K., Kumar, A., & Kumar, V. (2021). An optimal resource allocation model considering two-phase software reliability growth model with testing effort and imperfect debugging. Reliability: Theory & Applications, (SI 2 (64)), 241-255. DOI: 10.24412/1932-2321-2021-264-241-255
  • Tushar, J., Kumar, A., & Kumar, S. (2022). Approximations of quasi-linear elliptic optimal control problems on polygonal meshes under variational and virtual discretizations. International Journal of Applied and Computational Mathematics, 8(1), 1-35. DOI: https://doi.org/10.1007/s40819-021-01215-y
  • Tushar, J., Kumar, A., & Kumar, S. (2022). Variational and virtual discretizations of optimal control problems governed by diffusion problems. Applied Mathematics & Optimization, 85(2), 1-36. DOI: https://doi.org/10.1007/s00245-022-09872-1
  • Tushar, J., Kumar, A., & Kumar, S. (2022). Virtual element methods for general linear elliptic interface problems on polygonal meshes with small edges. Computers and Mathematics with Applications, 122, 61-75. DOI: https://doi.org/10.1016/j.camwa.2022.07.016
  • Kumar, A., Pani, A. K., & Joshi, M. C. (2022). Approximate Controllability of linear parabolic equation with memory. Computers and Mathematics with Applications, 128, 320-330. DOI: https://doi.org/10.1016/j.camwa.2022.11.003
  • Kumar, A., Latpate, S. G., & Sonawane, R. B. (2022). Controllability of a space-time fractional order parabolic equation. Discussiones Mathematicae: Differential Inclusions, Control and Optimization, 42 (2), 131-142. DOI: https://doi.org/10.7151/dmdico.1234
  • Pradhan, S. K., Kumar, A., & Kumar, V. (2023). An effort allocation model for a three-stage software reliability growth model. Predictive Analytics in System Reliability, 263-282. Cham: Springer International Publishing. DOI: https://doi.org/10.1007/978-3-031-05347-4_17
  • Tushar, J., Kumar, A., & Kumar, S. (2023). Virtual element methods for optimal control problems governed by elliptic interface problems, FIAM 2021, Springer Proceedings in Mathematics & Statistics, vol 410, 521-533, Springer, Singapore. DOI: https://doi.org/10.1007/978-981-19-7272-0_36
  • Tushar, J., Kumar, A., & Kumar, S. (2023). Mixed Virtual Element Methods for optimal control of Darcy flow. Computers and Mathematics with Applications, 140, 134-153. DOI: https://doi.org/10.1016/j.camwa.2023.04.022
  • Pradhan, S. K., Kumar, A., & Kumar, V. (2023). An optimal software enhancement and customer growth model: a control-theoretic approach. International J. of Quality & Reliability Management. DOI: https://doi.org/10.1108/IJQRM-08-2022-0240
  • Pradhan, S., Kumar, A., & Kumar, V. (2023). A testing coverage based SRGM subject to the uncertainty of the operating environment. In Computer Sciences & Mathematics Forum, Vol. 7, No. 1, p. 44. MDPI. EISSN No. 2813-0324. DOI: https://doi.org/10.3390/IOCMA2023-14436
  • Tushar, J., Sau, R. C. & Kumar, A. (2024). Virtual element method for control constrained Dirichlet boundary control problem governed by the diffusion problem. Journal of Scientific Computing, 98, 21. DOI: https://doi.org/10.1007/s10915-023-02410-3
  • Pradhan, S. K., Kumar, A., Kumar, V. & Kapur, P. K. (2024). Imperfect debugging, testing coverage, and compiler error-based SRGM with two types of faults under the uncertainty of the operating environment. In Reliability Engineering for Industrial Processes: An Analytics Perspective
    (pp. 361-380). Cham: Springer Nature Switzerland. DOI: https://doi.org/10.1007/978-3-031-55048-5_22
  • Pradhan, S. K., Kumar, A., & Kumar, V. (2024). Modelling Reliability Driven Software Release Strategy Considering Testing Effort with Fault Detection and Correction Processes: A Control Theoretic Approach. International Journal of Reliability, Quality and Safety Engineering. DOI: https://doi.org/10.1142/S0218539324400023.

Communicated:

  • Danumjaya, P., Kumar, A., & Pani, A. K. (2024). Asymptotic behaviour of the semidiscrete FE approximations to weakly damped wave equations with minimal smoothness on initial data. Communicated. arXiv: https://doi.org/10.48550/arXiv.2302.12476.
  • Pradhan, S. K., Kumar, A. & Kumar, V., A study on multi-release fault detection and change-point in fault correction process in software reliability analysis and optimal release time. Under review.
  • Pradhan, S. K., Kumar, A., & Kumar, V., A multi-release SRGM incorporating imperfect debugging and change-point with the simulated testing environment and software release time. Communicated.
  • Pradhan, S. K., Kumar, A., & Kumar, V., A general setup for modeling of multi-release SRGM with imperfect debugging, change point, and release time under simulated testing environment. Communicated.
  • Pradhan, S. K., Kumar, A., Kumar, V. & Kapur, P. K., Revisiting software reliability growth model under general setup. Communicated.
  • Pradhan, S. K., Kumar, A., & Kumar, V., Testing effort estimation through optimal control and parameter estimation techniques in software reliability growth modelling. Communicated.

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