Ninth MSU-UAB Conference on Differential Equations and Computational Simulations. Electron. J. Diff. Eqns., Conference 20 (2013), pp. 93-101. Title: Time-stepping for laser ablation Authors: Harihar Khanal (Embry-Riddle Aeronautical Univ., Daytona Beach, FL, USA) David Autrique (TU Kaiserslautern, Kaiserslautern, Germany) Vasilios Alexiades (Univ. of Tennessee, Knoxville, USA) Abstract: Nanosecond laser ablation is a popular technique, applied in many areas of science and technology such as medicine, archaeology, chemistry, environmental and materials sciences. We outline a computational model for radiative and collisional processes occurring during ns-laser ablation, and compare the performance of various low and high order time-stepping algorithms. Published October 31, 2013. Math Subject Classifications: 92C45, 35K60, 65M99. Key Words: Laser ablation; ode integration; time-stepper; peer methods; plasma formation, collisional radiative model.