This volume presents selected papers from the ninth International Conference on Spectral and High Order Methods (ICOSAHOM’12) conference that was held at Gammarth, Tunisia, during the week June 25–29, 2012. These selected papers were refereed by members of the scientific committee of ICOSAHOM as well as by other leading scientists. The first ICOSAHOM conference was held in Como, Italy, in 1989 and marked the beginning of an international conference series in Montpelier, France (1992); Houston, Texas, USA (1995); Tel Aviv, Israel (1998); Uppsala, Sweden (2001); Providence, Rhode Island, USA (2004); Beijing, China (2007); and Trondheim, Norway (2009). The ICOSAHOM conferences have established itself as the main meeting place for researchers with interest in the theoretical, applied and computational aspects of high-order methods for the numerical solution of partial differential equations. The number of registered participants for this most recent event, the first of its kind to be held at the African continent, exceeded 130, while the total number of talks was 105, comprising nine invited talks, 43 talks in nine different topic specific mini-symposia, and 53 talks in sessions devoted to contributed papers. The content of the proceedings is organized as follows. First, contributions from the invited speakers are included, listed in alphabetical order according to name of the invited speaker. Next, contributions from the speakers in mini-symposia and from contributed sessions are included and listed in alphabetical order according to the first author of each paper. The success of the meeting was ensured through the generous financial support by Institut de Mécanique et d’Ingénierie - Bordeaux, Laboratoire de Modélisation Mathématique et Numérique pour les Sciences de l’Ingénieur (LAMSIN), Ecole Nationale d’Ingénieurs de Tunis, Université de Tunis El Manar, Agence Nationale de Promotion de la Recherche en Tunisie, Laboratoire de Mathématiques Appliquées de Compiègne, Institut Français de Tunisie and European Office of Aerospace Research and Development, Air Force Office of Scientific Research (AFOSR) and US Air Force Research Laboratory (AFRL). Special thanks go to our colleagues and partners, Faker Ben Belgacem and Nabil Gmati, both central members of the organizing committee, who help enable and share with us this wonderful experience. Finally, the conference could not have happened without the invaluable support and assistance of the members and graduate students of LAMSIN.