Collocation in space and time: Experience with the Korteweg-de Vries equation
Based on the soliton solutions of the Korteweg-de Vries equation as a model problem the authors present numerical experiments with a collocation method in space and time. These methods lead to very efficient, fast and accurate algorithms if collocation takes place at the Gauss points. However, collocating at the Radau II points leads to significant phase and amplitude error due to the loss of conservativity. Besides implementation details comparisons with classical discretization methods are given.
scientific article; zbMATH DE number 1100601
scientific article