His PhD was on Wave Propagation and Stability for Finite Difference Schemes supervised by Joseph E. Oliger at Stanford University.
[13] His publications span a wide range of areas within numerical analysis and applied mathematics, including non-normal eigenvalue problems and applications, spectral methods for differential equations, numerical linear algebra, fluid mechanics, computational complex analysis, and approximation theory.
In 2013 he proposed a new formula to calculate the BMI of a person:[18][19] (International System of Units) Trefethen was the first winner of the Leslie Fox Prize for Numerical Analysis.
His research spans theory, algorithms, software and physical applications, particularly involving eigenvalues, pseudospectra – a concept which he introduced – and dynamics.
He has also made major contributions to finite difference and spectral methods for partial differential equations, numerical linear algebra, and complex analysis.