Analysis of error control strategies for continuous Runge-Kutta methods
SIAM Journal on Numerical Analysis
Practical Runge-Kutta processes
SIAM Journal on Scientific and Statistical Computing
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
The tolerance proportionality of adaptive ODE solvers
Journal of Computational and Applied Mathematics - Special issue on numerical methods for ordinary differential equations
Numerical investigations on global error estimation for ordinary differential equations
ICCAM '96 Proceedings of the seventh international congress on Computational and applied mathematics
Global Error Estimates for Ordinary Differential Equations
ACM Transactions on Mathematical Software (TOMS)
Parallel Two-Step W-Methods with Peer Variables
SIAM Journal on Numerical Analysis
Error Estimation and Control for ODEs
Journal of Scientific Computing
Nordsieck methods on nonuniform grids: stability and order reduction phenomenon
Mathematics and Computers in Simulation
On Global Error Estimation and Control for Initial Value Problems
SIAM Journal on Scientific Computing
Explicit two-step peer methods
Computers & Mathematics with Applications
Global error estimation based on the tolerance proportionality for some adaptive Runge-Kutta codes
Journal of Computational and Applied Mathematics
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
Rosenbrock-type 'Peer' two-step methods
Applied Numerical Mathematics
Doubly quasi-consistent parallel explicit peer methods with built-in global error estimation
Journal of Computational and Applied Mathematics
Variable-Stepsize Interpolating Explicit Parallel Peer Methods with Inherent Global Error Control
SIAM Journal on Scientific Computing
Partially implicit peer methods for the compressible Euler equations
Journal of Computational Physics
Global error estimation and control in linearly-implicit parallel two-step peer W-methods
Journal of Computational and Applied Mathematics
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
Adaptive ODE solvers in extended Kalman filtering algorithms
Journal of Computational and Applied Mathematics
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This paper elaborates a global error estimation and control mechanism in explicit two-step peer methods. These recently designed methods exhibit their high efficiency even in comparison to the best explicit Runge-Kutta pairs. More precisely, we form here triples of the so-called superconvergent explicit peer schemes and show that they are cheap and able to achieve preassigned accuracy conditions in automatic mode. For comparison, we present also numerical data derived by built-in explicit Matlab ODE solvers implemented with only local error control. Especially, we point out that a scaled global error is computed and regulated in this paper in contrast to the earlier published results where the absolute values of the global error have been utilized.