• Partial Differential Equations Constrained Optimal Control Problems (related Analysis and Numerics)
• Mathematical Modelling with Ordinary Differential Equations and Partial Differential Equations.
• Computational Fluid Dynamics.
• Free Boundary Value Problems.
•  Infectious Disease Epidemiology, Analysis and Numerics

 Publications:

 Journal publications:

 1. Optimal Control Strategies for Diabetes Population Management”, submitted to International Journal of Mathematical Population Studies at Taylor & Francis, November 2023.

2. E.M. Ranatunga, N.K. Hettiarachchi, M.K. Abeyratne, and M.C.S. Fernando, “Investigation of the Influence of Inner Geometries of the Receiver Tube of a Parabolic Trough Collector System Used for Water Heating”, ENGINEER- The Journal of the Institution of Engineers, Sri Lanka - Vol. LVI, No. 04, pp. [105-119], 2023.

3. L. W. Somathilaka, and M. C. S. Fernando.‘Optimal quarantine, isolation, and social distancing strategies for COVID-19 based on a mathematical model’, Int. J. Mathematical Modelling and Numerical Optimisation, Vol. 12, No. 4, pp.349–367, 2022.

4. R. M. R. M. Jayathilaka, M. C. S. Fernando. " Numerical modeling of the spatial variation of sediment transport using wave climate schematization method-a case study

of west coast of Sri Lanka." Journal of the National Science Foundation of Sri Lanka 47,no. 4, 421-433, 2019.

5. S. Panda, M. Sellier, M. C. S. Fernando, M. K. Abeyratne. "Process parameter identification in thin film flows driven by a stretching surface." International Journal of

Engineering Mathematics, Volume 2014, Article ID 485431, 12 pages, 2014.

1. Undergrad-level research titled “Numerical Modelling Approach in Investigating Lagoon Water Salinity Profile in Sri Lanka”, collaboration work with NARA, Sri Lanka (from

August 2023 to Present).

2. Undergrad-level research titled “Optimal control of drug diffusion through the compartments of blood and tissue medium” (from August 2023 to Present).

3. Postgraduate-level research titled “Development of a solar-powered water distillation system with a parabolic trough reflector and optimized receiver geometry”, collaboration

work with the Department of Engineering, University of Ruhuna, UGC grant number PG2017(I)/RUH/02 (from January 2020 to Present).

1. Wasantha Mohotti Memorial Gold Medal awarded by Dr. J. E. Mohotti to the graduate who obtained a First Class Honours with the highest aggregate marks in the Bachelor of

Science Degree Examination in Physical Science held in 2010.

2. Mallika De Mel Memorial Gold Medal awarded by the Ronnie De Mel Trust Fund to the graduate who obtained a First Class Honours with the highest aggregate marks in the

Final Examinations leading to the Degree of Bachelor of Science held in 2010.

3.Professor Isabelle Attali Memorial, CIMPA (International Center for Pure and Applied Mathematics, France) Gold Medal for the outstanding graduate who scored the highest aggregate marks at the B.Sc. (Special) Degree Examination in Mathematics with First Class (Honours), in the year 2010, awarded by the Educational Support Foundation- Ruhuna Mathematics.

1. Co-supervisor of the postgraduate degree leading to a Ph.D. of the Student E.M. Ranathunga, Department of Physics, Faculty of Science, University of Ruhuna, UGC grant number PG2017(I)/RUH/02, 2019- present.
2. A reviewer and convener at the 10 th Ruhuna International Science and Technology Conference, Sri Lanka, 2023.
3. An external reviewer of the M.Phil degree of Ms. H.K. Abeynanda, Faculty of Graduate Studies, University of Sri Jayewardenepura, Registration number: 1450PS2017004, 2022.
4. A reviewer and convener at the 9 th Ruhuna International Science and Technology Conference, Sri Lanka, 2022.
5. A reviewer in ICAPS 2021, International Conference on Applied and Pure Science organized by the Faculty of Science, University of Kelaniya, 2021.
6. A reviewer in ICMAS 2021, an International Conference organized by the Faculty of Science, University of Colombo, 2021
7. A reviewer in the Journal of the National Science Foundation of Sri Lanka, 2020
8. An editorial Assistant in the Ruhuna Journal of Science, 2020-2023.
9. A reviewer and convener at the 7 th Ruhuna International Science and Technology Conference, Sri Lanka, 2020.
10. A reviewer at the 6 th Ruhuna International Science and Technology Conference, Sri Lanka, 2019.