Al Marzouk, A.A. Erdelyi, B. JACoW Geneva, Switzerland 978-3-95450-180-9 10.18429/JACoW-NAPAC2016-TUPOB14 English 514-517 TUPOB14 ion proton software operation simulation Contribution to a conference proceedings 2017 2017-01 http://dx.doi.org/10.18429/JACoW-NAPAC2016-TUPOB14 https://jacow.org/napac2016/papers/tupob14.pdf We are developing a new numerical integrator based on Picard iteration method for Coulomb collisions. The aim is to achieve a given prescribed accuracy most efficiently. The integrator is designed to have adaptive time stepping, variable order, and dense output. It also has an automatic selection of the order and the time step. We show that with a good estimation of the radius of convergence of the expansion, we can obtain the optimal time step size. We also show how the optimal order of the integration is chosen to maintain the required accuracy. For efficiency, particles are distributed over time bins and propagated accordingly.