Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Numerical investigations on global error estimation for ordinary differential equations
ICCAM '96 Proceedings of the seventh international congress on Computational and applied mathematics
Explicit, Time Reversible, Adaptive Step Size Control
SIAM Journal on Scientific Computing
Constant coefficient linear multistep methods with step density control
Journal of Computational and Applied Mathematics
On Global Error Estimation and Control for Initial Value Problems
SIAM Journal on Scientific Computing
Explicit two-step peer methods
Computers & Mathematics with Applications
Superconvergent explicit two-step peer methods
Journal of Computational and Applied Mathematics
On quasi-consistent integration by Nordsieck methods
Journal of Computational and Applied Mathematics
Time-step selection algorithms: Adaptivity, control, and signal processing
Applied Numerical Mathematics
On the derivation of explicit two-step peer methods
Applied Numerical Mathematics
Variable-Stepsize Interpolating Explicit Parallel Peer Methods with Inherent Global Error Control
SIAM Journal on Scientific Computing
Global Error Control in Adaptive Nordsieck Methods
SIAM Journal on Scientific Computing
Variable-stepsize doubly quasi-consistent parallel explicit peer methods with global error control
Applied Numerical Mathematics
Local and global error estimation and control within explicit two-step peer triples
Journal of Computational and Applied Mathematics
| Hi-index | 7.29 |
Recently, Kulikov presented the idea of double quasi-consistency, which facilitates global error estimation and control, considerably. More precisely, a local error control implemented in such methods plays a part of global error control at the same time. However, Kulikov studied only Nordsieck formulas and proved that there exists no doubly quasi-consistent scheme among those methods. Here, we prove that the class of doubly quasi-consistent formulas is not empty and present the first example of such sort. This scheme belongs to the family of superconvergent explicit two-step peer methods constructed by Weiner, Schmitt, Podhaisky and Jebens. We present a sample of s-stage doubly quasi-consistent parallel explicit peer methods of order s-1 when s=3. The notion of embedded formulas is utilized to evaluate efficiently the local error of the constructed doubly quasi-consistent peer method and, hence, its global error at the same time. Numerical examples of this paper confirm clearly that the usual local error control implemented in doubly quasi-consistent numerical integration techniques is capable of producing numerical solutions for user-supplied accuracy conditions in automatic mode.