One-leg variable-coefficient formulas for ordinary differential equations and local–global step size control

2006 ◽  
Vol 43 (1) ◽  
pp. 99-121 ◽  
Author(s):  
Gennady Yu. Kulikov ◽  
Sergey K. Shindin
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Variable Coefficient ◽  
Size Control ◽  
Step Size ◽  
Step Size Control

One-leg Integration of Ordinary Differential Equations with Global Error Control

2005 ◽  
Vol 5 (1) ◽  
pp. 86-96 ◽  
Author(s):  
Gennady Yu. Kulikov ◽  
Sergey K. Shindin
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Error Control ◽  
Size Control ◽  
Adaptive Algorithms ◽  
Reasonable Accuracy ◽  
Step Size ◽  
Step Size Control ◽  
The Family

AbstractIn this paper we study the family of one-leg two-step second-order methods developed by Dahlquist et al., which possess the A-stability and G-stability properties on any grid. These methods are implemented with the local-global step size control derived by Kulikov and Shindin with the aim to obtain automatically the numerical solution with any reasonable accuracy set by the user. We show that the error control is more complicated in one-leg methods, especially when applied to stiffproblems. Thus, we adapt our local-global step size control for the methods indicated above and test these adaptive algorithms in practice.

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