Accepted Articles:
- Bariwal, S.K., Hussain, S. & Kumar, R. (2024). Non-linear collision-induced breakage equation: finite volume and semi-analytical methods. Acta Applicandae Mathematicae.
- Shweta, Hussain, S., Kumar, R. & Kumar, R. (2024). An improved version of homotopy perturbation method for multi-dimensional Burgers’ equations. Journal of Applied analysis and Computation.
Published Articles:
- Saddam Hussain, Sanjiv Kumar Bariwal, Rajesh Kumar (2025). Collisional breakage population balance equation: An analytical
approach. J. Math. Anal. Appl. 541, 128697.
- Hussain, S., Shweta, & Kumar, R. (2024). An analytical treatment to spatially inhomogeneous population balance model. Chaos, Solitons & Fractals, 186, 115229. https://doi.org/10.1016/j.chaos.2024.115229.
- Sonali Kaushik & Rajesh Kumar (2024). Qualitative Analysis of a New Numerical Method to Solve Ordinary Differential Equations”, International Journal of Applied and Computational Mathematics, 10 (3), 99.
- Hussain, S., & Kumar, R. (2024). Elzaki projected differential transform method for multidimensional aggregation and combined aggregation-breakage equations. Journal of Computational Science, 75, 102211. https://doi.org/10.1016/j.jocs.2024.102211.
- Hussain, S., Arora, G., & Kumar, R. (2024). An efficient semi-analytical technique to solve multidimensional Burgers’ equation. Computational and Applied Mathematics, 43(1), 11.
- Arora, G., Kumar, R., & Mammeri, Y. (2024). Elzaki Transform Based Accelerated Homotopy Perturbation Method for Multi-dimensional Smoluchowski’s Coagulation and Coupled Coagulation-fragmentation Equations. Journal of Applied Analysis and Computation, 14(5), 1-32.
- Kaushik S, Kumar R. (2023). A Novel Optimized Decomposition Method for Solving Smoluchowski’s Aggregation Equation. Journal of Computational and Applied Mathematics, 419: 114710.
- Sonali Kaushik, Rajesh Kumar & Fernando P. da Costa (2023). Theoretical Analysis of a Discrete Population Balance Model for Sum Kernel. Portugaliae Mathematicae, 80 (3), 347-367.
- Sonali Kaushik & Rajesh Kumar (2023). Steady-State Solution for Discrete Oort-Hulst-Safronov Coagulation Equation. Int. J. of Dynamical Systems and Differential Equations, 13(2), 144-163.
- Hussain, S., Arora, G., & Kumar, R. (2023). Semi-analytical methods for solving non-linear differential equations: a review. Journal of Mathematical Analysis and Applications, 127821. https://doi.org/10.1016/j.jmaa.2023.127821
- Kaushik, S., Hussain, S., & Kumar, R. (2023). Laplace transform-based approximation methods for solving pure aggregation and breakage equations. Mathematical Methods in the Applied Sciences, 46(16), 17402–17421. https://doi.org/10.1002/mma.9507.
- Sonali Kaushik & Rajesh Kumar (2023). Optimized Decomposition Method for Solving Multi-Dimensional Burgers’ Equation.Mathematics and Computers in Simulation, 208, 326-350.
- Sanjiv Kr. Bariwal, Prasanta Kr. Barik, Ankik Kr. Giri, Rajesh Kumar (2023). Finite volume convergence analysis for coagulation-fragmentation equations with singular rates. Journal of Hyperbolic Differential Equations, no. 20, 793-823.
- Arora, G., Hussain, S., & Kumar, R. (2023). Comparison of variational iteration and Adomian decomposition methods to solve growth, aggregation and aggregation-breakage equations. Journal of Computational Science, 67, 101973. https://doi.org/10.1016/j.jocs.2023.101973
- Arora, G., Kumar, R., & Mammeri, Y. (2023). Homotopy perturbation and adomian decomposition methods for condensing coagulation and Lifshitz-Slyzov models. GEM-International Journal on Geomathematics, 14(1), 4. https://link.springer.com/article/10.1007/s13137-023-00215-y
- Choudhary K K, Kumar R, Kumar R. (2023). Analysis of a prion proliferation model with polymer coagulation in the presence of chaperone. Mathematical Methods in the Applied Sciences, Vol 46:13027-13050.
- Kapil Kumar Choudhary, Rajiv Kumar and Rajesh Kumar (2022). Global classical and weak solutions of a prion proliferation model in the presence of chaperone in a Banach space. Evolution Equations and Control Theory, doi:10.3934/eect.2021039.
- Kapil Kumar Choudhary, Rajiv Kumar and Rajesh Kumar (2022). Weak solution and global qualitative behaviour of a prion proliferation model in the presence of chaperone. Acta Applicandae Mathematicae, doi:10.1007/s10440-022-00512-y.
- Sonali Kaushik & Rajesh Kumar (2022). Existence, Uniqueness and Mass Conservation for Safronov- Dubovski Coagulation Equation. Acta Applicandae Mathematicae. 179(1) 1-21.
- Bariwal S. K., Kumar R. (2022). Convergence and error estimation of weighted finite volume scheme for coagulation-fragmentation equation. Numerical Methods for PDEs, 39:2561-2583.
- Nabil Bedjaoui, Rajesh Kumar, Youcef Mammeri (2021). Asymptotic behavior of solution of Whitham-Broer-Kaup type equations with negative dispersion. Journal of Applied Analysis. https://doi.org/10.1515/jaa-2021-2066.
- Prasanta Kumar Barik, Ankik Kumar Giri and Rajesh Kumar (2021). Mass-conserving weak solutions to the coagulation and collisional breakage equation with singular rates. Kinetic and Related Models, 14(2).
- Rajiv Kumar, Kapil Kumar Choudhary and Rajesh Kumar (2021). Study of the solution of a semilinear evolution equation of a prion proliferation model in the presence of chaperone in a product space. Mathematical Methods in the Applied Sciences, 44, 1942–1955.
- Rajesh Kumar*, Vikrant Surasani and Y. P. Gokhale (2020). Population balance modeling with coupled agglomeration and disintegration processes for TiO2 nanoparticles formation and experimental validation, Journal of Cluster Science Including Nanoclusters and Nanoparticles, DOI: 10.1007/s10876-020-01895-4.
- Rajesh Kumar*, Souvik Ghosh, Abhijit Datta Banik (2020). Numerical Study on Transient Behavior of Finite Bulk Arrival or Service Queues with Multiple Working Vacations. Int. J. of Mathematics in Operational Research, Inderscience, 384-403.
- Suresh Pathi, Rajesh Kumar, Vikranth Kumar Surasani (2020). Investigation on agglomeration kinetics of acetaminophen using fluidized bed wet granulation. Asia-Pacific Journal of Chemical Engineering, https://doi.org/10.1002/apj.2416.
- Rajesh Pradhan, Siddhanth Hejmady, Rajeev Taliyan, Rajesh Khadgawat, Tarang Gupta, Garima Kachhawa, Rajesh Kumar, Gautam Singhvi & Sunil Kumar Dubey (2020). Simultaneous estimation of parabens and bisphenol a in ready-to-eat foodstuffs by using QbDdriven high-pressure liquid chromatography method. International Journal of Environmental Analytical Chemistry, https://doi.org/10.1080/03067319.2020.1756272.
- Daniel Kressner, Rajesh Kumar, Fabio Nobile and Christine Tobler (2015). Low rank tensor approximation for high-order correlation functions of Gaussian random fields. SIAM/ASA J. Uncertainty Quantification 3(1), 393-416.
- Rajesh Kumar, Jitendra Kumar and Gerald Warnecke (2014). Convergence analysis of a finite volume scheme for solving non-linear aggregation-breakage population balance equations, Kinetic and Related Models 7(4), 713-737.
- Rajesh Kumar, Jitendra Kumar and Gerald Warnecke (2013). Moment preserving finite volume schemes for solving population balance equations incorporating aggregation, breakage, growth and source terms, Mathematical Models and Methods in Applied Sciences 23(07), 1235-1273.
- Rajesh Kumar and Jitendra Kumar (2013). Numerical simulation and convergence analysis of a finite volume scheme for solving general breakage population balance equations, Applied Mathematics and Computation 219(10), 5140-5151.
- Rajesh Kumar and Jitendra Kumar (2013). A population balance model with simultaneous aggregation and breakage for the synthesis of Titanium dioxide nanoparticles, Indian Journal of Indus. & Appl. Math. 4(1), 71-81, 2013. Special issue dedicated to Prof. Helmut Neunzert.
- Rajesh Kumar and Jitendra Kumar (2012). Finite volume scheme for multiple fragmentation equations, Int. Journal of Numerical Analysis and Modeling 3(3), 270-284, 2012.
- Rajesh Kumar, Jitendra Kumar and Gerald Warnecke (2011). Numerical methods for solving twodimensional aggregation population balance equations, Computers and Chemical Engineering Science 35, 999-1009.
- Gokhale, R. Kumar, J. Kumar, W. Hintz, G. Warnecke and J. Tomas (2009). Disintegration process of surface stabilized sol-gel TiO2 nanoparticles by population balances, Chemical Engineering Science 64, 5302-5307.
Book Chapters:
- Sonali Kaushik & Rajesh Kumar, “Global Uniqueness Theorem for a Discrete Population Balance Model with Application in Astrophysics”, Advances in Computational Modeling and Simulation, (Conference Proceedings) 61-73, (2022). https://link.springer.com/chapter/10.1007/978-981-16-7857-8_6
Published Book (Monograph):
1. Numerical analysis of finite volume schemes for population balance equations, Docupoint Wissenschaft, Magdeburg, Germany, ISBN-978-3869121055, PhD Thesis 2012.
Technical Report/Theses:
1. D. Kressner, R. Kumar, F. Nobile and C. Tobler: Low rank tensor approximation for high order correlation functions of Gaussian random fields, Mathicse Technical Report, EPFL, Switzerland, No. 24, 2014.
2. T. A. Airaksinen, Yu He, T. W. Kinyanjui, R. Kumar, K. Ristic, C. A. Zarzer: Paint Drying With UV Rays. ECMI modelling week report. Copy available at
An Institute of Eminence
