A New Efficient Explicit Deferred Correction Framework: Analysis and Applications to Hyperbolic PDEs and Adaptivity.

ABSTRACT: The deferred correction (DeC) is an iterative procedure, characterized by increasing the accuracy at each iteration, which can be used to design numerical methods for systems of ODEs. The main advantage of such framework is the automatic way of getting arbitrarily high order methods, which can be put in the Runge-Kutta (RK) form. The drawback is the larger computational cost with respect to the most used RK methods. To reduce such cost, in an explicit setting, we propose an efficient modification: we introduce interpolation processes between the DeC iterations, decreasing the computational cost associated to the low order ones. We provide the Butcher tableaux of the new modified methods and we study their stability, showing that in some cases the computational advantage does not affect the

SUBMITTER: Micalizzi L 

PROVIDER: S-EPMC11637013 | biostudies-literature | 2024

REPOSITORIES: biostudies-literature