In this paper, we describe an approach to estimate the global error for explicit second derivative general linear methods based on the approach which has been already used for global error estimation of explicit general linear methods. In this approach, to estimate the global error, we use the numerical solutions of pairs of second derivative general linear methods with the same order and stage order that are constructed such that their global error functions are proportional. Numerical experiments demonstrate the excellent agreement of the global error estimation with the exact one in both constant and variable stepsize environments.
Global error estimation for explicit second derivative general linear methods / Abdi, A.; Hojjati, G.; Izzo, G.; Jackiewicz, Z.. - In: NUMERICAL ALGORITHMS. - ISSN 1017-1398. - (2022). [10.1007/s11075-021-01211-9]
Global error estimation for explicit second derivative general linear methods
Izzo G.;
2022
Abstract
In this paper, we describe an approach to estimate the global error for explicit second derivative general linear methods based on the approach which has been already used for global error estimation of explicit general linear methods. In this approach, to estimate the global error, we use the numerical solutions of pairs of second derivative general linear methods with the same order and stage order that are constructed such that their global error functions are proportional. Numerical experiments demonstrate the excellent agreement of the global error estimation with the exact one in both constant and variable stepsize environments.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.