Journal articles
Numerical Approximation of Riemann Problems for a Liquid–Gas Two-Phase Isentropic Flow Model: Computational Assessment of Three Explicit Numerical Schemes
Abdul Rab, Saleem Ahmed Naich, and Shah Rukh. Spectrum of Engineering Sciences, 4(3), 7215–7229 (2026).
Computational comparison of Lax–Friedrichs, Lax–Wendroff, and FORCE methods using matched numerical benchmarks and conservation checks.
Mathematical Modelling and Simulation of HIV Dynamics
Abdul Rab, Saleem Ahmed Naich, and Shah Rukh. Spectrum of Engineering Sciences, 4(1) (2026).
Mathematical analysis of within-host HIV dynamics, including equilibrium stability, treatment efficacy, and numerical simulations using the fourth-order Runge–Kutta method.
Preprints & thesis research
Numerical Solution to the Riemann Problem for the Liquid–Gas Two-Phase Isentropic Flow Model
Studied a coupled nonlinear flow system numerically in Python using Lax–Friedrichs, Lax–Wendroff, and FORCE schemes. This research is related to the published 2026 article above.
arXiv:2512.02071 ↗Mathematical Modeling and Simulation of HIV Dynamics
Earlier B.S. thesis research and a related arXiv preprint, preceding the published journal article listed above.
arXiv:2512.13171 ↗Research interests
- Numerical methods for partial differential equations
- Hyperbolic conservation laws and Riemann solvers
- High-resolution and finite-volume schemes
- Multiphase flow and mathematical modeling
- Mathematical biology and dynamical systems
- Stability, convergence, error analysis, and reproducible scientific computing
Research interests describe directions I am pursuing, not additional completed publications.