In the context of the numerical integration of initial value problems based on ordinary differential equations, it is the purpose of this paper to introduce a modification of two-step collocation methods, in order to obtain coefficient matrices with a structured shape, to get an efficient implementation. Our aim is the development of new collocation-based methods having high order of convergence and strong stability properties (e.g. A-stability and L-stability). We present the constructive technique, discuss the order of convergence and the stability properties of the resulting methods and provide some numerical results confirming the theoretical expectations. Â© 2012 IMACS.
|Titolo:||Two-step modified collocation methods with structured coefficient matrices|
|Data di pubblicazione:||2012|
|Appare nelle tipologie:||1.1 Articolo in rivista|