TY - JOUR
T1 - Global error estimation for explicit second derivative general linear methods
AU - Abdi, Ali
AU - Hojjati, Gholamreza
AU - Izzo, Giuseppe
AU - Jackiewicz, Zdzislaw
N1 - Funding Information:
The work of the first and second authors was supported by the University of Tabriz, International and Academic Cooperation Directorate, in the framework of TabrizU-300 program.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2022/6
Y1 - 2022/6
N2 - 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.
AB - 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.
KW - Fixed-stepsize methods
KW - General linear methods
KW - Global error estimation
KW - Inherent Runge–Kutta stability
KW - Ordinary differential equations
KW - Second derivative methods
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U2 - 10.1007/s11075-021-01211-9
DO - 10.1007/s11075-021-01211-9
M3 - Article
AN - SCOPUS:85118613469
SN - 1017-1398
VL - 90
SP - 833
EP - 850
JO - Numerical Algorithms
JF - Numerical Algorithms
IS - 2
ER -