based on equidistribution principles as originally introduced by White [23].
Previous contributions in this area
This paper proposes a method of lines solution procedure with time and space adaptation for one-dimensional systems of partial include Sanz-Serna and Christie [20] and Revilla [16] who differential equations whose solutions display steep moving fronts.
study the numerical solution of the cubic Schro ¨dinger equa-The spatial remeshing algorithm, which is a variation of the method tion (CSE) in one spatial dimension. Their experiments published by Sanz-Serna and Christie and an extension suggested demonstrate clearly the benefits of the adaptation in space, by Revilla, is a static remeshing method based on equidistribution resulting in a reduction of the number of nodes by a factor principles. The selection of the several algorithm components, i.e., grid placement criterion, spatial discretization scheme, time inte-4 to 12 (depending on the example considered and on the grator, adaptation frequency, and parameter tuning, are investichoice of the function to be equidistributed) in comparison gated and illustrated with several test examples, i.e., the cubic to that required by similar fixed-grid methods. Schro ¨dinger equation, a model of a single-step reaction with diffu-Starting with the spatial remeshing technique proposed sion, and a model of flame propagation.