Experimentation of a finite volume method approach with an adaptive moving mesh

Abstract

This work constitutes a realization of the thought that through numerical analysis mathematics has become an experimental science. In fact, we are testing a new approach to numerical resolution of mathematical problems. The main aim is to highlight its advantages compared to the traditional approach. We have thus experimented with an approach consisting of the principle of the finite volumes method described by J. A. Mackenzie combined with an adaptive moving mesh method, so the principle has been described and used by several other authors, such as H. TANG and T. TANG. The test problem considered was that of Burgers, which we have already used in our previous work but not with the same approach as the one considered here. This time, the results are more than satisfactory.