Abel Okojunu

I am a doctoral candidate in Applied and Computational Mathematics at Florida State University. My dissertation, Global Linear Stability Analysis of Capillary-Driven Interfacial Instability: A Jacobian-Free Approach, uses matrix-free Krylov and Arnoldi methods: numerical linear algebra techniques that allow an instability to be analyzed without explicitly forming the Jacobian of the system governing the flow.

I completed my undergraduate studies in Mathematics at the Federal University of Petroleum Resources, Nigeria, where a thesis on compact finite-difference schemes first directed my attention toward numerical methods for partial differential equations. That interest has since developed outside the classroom in two settings: a summer appointment at Lawrence Livermore National Laboratory, where I applied the Sherman-Morrison formula to accelerate an ordinary differential equation (ODE) solver for sustainable-aviation modeling, and several years as a graduate teaching assistant and instructor of record at Florida State University, where I teach calculus and applied linear algebra.

My present interests include stiff ODE solvers, uncertainty quantification, domain decomposition, Bayesian inverse problems, and the conditions under which physics-informed neural networks justify their computational cost relative to classical solvers. I develop these questions at greater length on the blog, where the emphasis falls on the trade-offs each method entails, not on advocacy for any single approach.

Further material appears on the projects and publications pages. I welcome correspondence concerning numerical linear algebra, computational fluid dynamics, high-performance computing, and scientific computing more generally.