This special issue of Numerical Algorithms is devoted to the Auckland Numerical ODEs Conference (ANODE 2018), which was held in Auckland, New Zealand, February 19–23, 2018. This conference was organized by Saghir Ahmad from Information Technology, Auckland Institute for Studies, and John Butcher, Gulshad Imran, Nicolette Rattenbury, and Shixiao Wang, from the Department of Mathematics of the University of Auckland. It was attended by 55 participants from 14 countries (Australia, Canada, China, France, Germany, Italy, Japan, Malaysia, New Zealand, Norway, Spain, Taiwan, UK, and the USA). The scientific program of this meeting consisted of 40 talks in the areas related to the numerical analysis of differential equations.

This special issue contains 22 of the papers that have been presented at this conference. In selecting these papers, we followed the regular refereeing process for the journal. We would like to express our gratitude for the help of many reviewers as to guarantee the high quality of these papers. We would also like to thank the editor-in-chief, Professor Claude Brezinski, for offering the possibility to publish this special issue of Numerical Algorithms.