New Adaptive Exponential Propagation Iterative Methods of Runge-Kutta Type. - Mayya Tokman; John Loffeld; Paul Tranquilli (SIAM J. Sci. Comput., 2012)

CUDA acceleration of a matrix-free Rosenbrock-K method applied to the shallow water equations. - Paul Tranquilli; Ross Glandon; Adrian Sandu (ScalA@SC, 2013)

Solving stochastic chemical kinetics by Metropolis Hastings sampling. - Azam S. Zavar Moosavi; Paul Tranquilli; Adrian Sandu (CoRR, 2014)

Lightly Implicit Krylov-Exponential (LIKE) Methods. - Paul Tranquilli; Adrian Sandu (CoRR, 2014)

Exponential-Krylov methods for ordinary differential equations. - Paul Tranquilli; Adrian Sandu (J. Comput. Phys., 2014)

Rosenbrock-Krylov Methods for Large Systems of Differential Equations. - Paul Tranquilli; Adrian Sandu (SIAM J. Sci. Comput., 2014)

Application of approximate matrix factorization to high order linearly implicit Runge-Kutta methods. - Hong Zhang 006; Adrian Sandu; Paul Tranquilli (J. Comput. Appl. Math., 2015)

A Numerical Investigation of Matrix-Free Implicit Time-Stepping Methods for Large CFD Simulations. - Arash Sarshar; Paul Tranquilli; Brent Pickering; Andrew McCall; Adrian Sandu; Christopher J. Roy (CoRR, 2016)

Analytical Jacobian-vector products for the matrix-free time integration of partial differential equations. - Paul Tranquilli; Ross Glandon; Arash Sarshar; Adrian Sandu (J. Comput. Appl. Math., 2017)

Biorthogonal Rosenbrock-Krylov time discretization methods. - Ross Glandon; Paul Tranquilli; Adrian Sandu (CoRR, 2019)

Adaptive Krylov-Type Time Integration Methods. - Paul Tranquilli; Ross Glandon; Adrian Sandu (CoRR, 2019)

EPIRK-W and EPIRK-K Time Discretization Methods. - Mahesh Narayanamurthi; Paul Tranquilli; Adrian Sandu; Mayya Tokman (J. Sci. Comput., 2019)

Subspace adaptivity in Rosenbrock-Krylov methods for the time integration of initial value problems. - Paul Tranquilli; Ross Glandon; Adrian Sandu (J. Comput. Appl. Math., 2021)

A deterministic verification strategy for electrostatic particle-in-cell algorithms in arbitrary spatial dimensions using the method of manufactured solutions. - Paul Tranquilli; Lee F. Ricketson; Luis Chacón (J. Comput. Phys., 2022)