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Dr. Amila Muthunayake

Education

Contact Information

Email: amilamuthunayake@weber.edu
Phone: 801-626-7107
Office Location: 
Tracy Hall Science Center (TY)
Room 381N

Teaching Philosophy & Focus

I consider teaching as an opportunity to help students not only to learn but to think about what and why they are learning. I attempt to make students understand mathematical (statistical) concepts and to answer the question of why we are studying particular concepts by making connections to real-life applications.

Courses Taught

Research Areas of Interest

My current research interests are in Elliptic Partial Differential Equations, Numerical Analysis and Physics-informed Neural Networks and their applications in Ecology.

Current Projects

1) Radial finite difference methods for approximating solutions of sublinear semipositone problems in a ball.

2) The diffusive Lotka-Volterra competition model in fragmented patches: Coexistence

3) The diffusive Lotka-Volterra predator-prey model in fragmented patches: Coexistence

Publications

1) J. T. Cronin, J. Goddard II, A. Muthunayake and R. Shivaji, Modeling the effects of trait- mediated dispersal on coexistence of mutualists, J. Mathematical Biosciences and Engineering, 2020, Vol. 17, Issue 6 : 7838-7861, doi:10.3934/mbe.2020399.

2) N. Fonseka, A. Muthunayake, R. Shivaji and B. Son, Singular reaction diffusion equations where a parameter influences the reaction term and the boundary condition, J. Topological Methods in Nonlinear Analysis, 2020, Vol. 57, No.1 pp. 221 - 242, doi:10.12775/TMNA.2020.022.

3) Ujjal Das, A. Muthunayake, R. Shivaji, Existence results for a class of p-q Laplacian semi- positone boundary value problems, Electronic Journal of Qualitative Theory of Differential Equations, 2020, No. 88, pp. 1-7, doi:10.14232/ejqtde.2020.1.88.

4) D.D. Hai, A. Muthunayake, R. Shivaji, A uniqueness result for a class of infinite semiposi- tone problems with nonlinear boundary conditions, Positivity, 2021, doi:10.1007/s11117-021-00820-x.

5) A. Muthunayake, C. Phan and R. Shivaji, An infinite semipositone problem with a reversed S-shaped bifurcation curve, 2022, Electronic Research Archive.