Section: New Results

High order linearly implicit methods for evolution problems

In [31], I. Lacroix and G. Dujardin have developed a new class of numerical integration methods for evolution problems. This class contains methods of arbitrarily high order that only require the solution of a linear system per time step. For evolution ODEs (Cauchy problems), they give a constructive proof of existence for such arbitrarily high order methods. For evolution PDEs, they demonstrate numerically that these new methods can outperform high order methods from the literature on several test cases.