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
Matlab Guide
Nordsieck methods on nonuniform grids: stability and order reduction phenomenon
Mathematics and Computers in Simulation
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
Doubly quasi-consistent parallel explicit peer methods with built-in global error estimation
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
Local and global error estimation and control within explicit two-step peer triples
Journal of Computational and Applied Mathematics
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In this paper, we present variable-stepsize explicit parallel peer methods grounded in the interpolation idea. Approximation, stability, and convergence are studied in detail. In particular, we prove that some interpolating peer methods are stable on any variable mesh in practice. Double quasi consistency is utilized to introduce an efficient global error estimation formula in the numerical methods under discussion. The main advantage of these new adaptive schemes is the fact that the leading terms of their local and true errors coincide. Thus, controlling the local error of such methods by cheap standard techniques automatically regulates their global error as well. Numerical experiments of this paper support theoretical results presented below and illustrate how the new global error control concept works in practice. We also conduct a comparison with explicit ODE solvers in MATLAB.