Abdulle earned a doctorate in mathematics under Gerhard Wanner and Ernst Hairer at the University of Geneva with the thesis Méthodes de Chebyshev basées sur des polynômes orthogonaux.
From 2001 to 2002, he was a postdoctoral researcher at Princeton University and worked at the computational laboratory at ETH Zurich from 2002 to 2003.
[5] Abdulle was impassioned with modeling and numerical simulations in biology, chemistry, geology, and medicine.
[9][10] He also invented the Orthogonal Runge-Kutta-Chebyshev,[11] which was used to solve stiff differential equations which were then generalized to multiscale stochastic systems.
[12][13] In 2005, Abdulle won the New Talent Award at the International Conference on Scientific Computation and Differential Equations.