The Numerical Analysis of Ordinary Differential Equations; Runge-Kutta and General Linear Methods.

1988 ◽  
Vol 51 (183) ◽  
pp. 377 ◽  
Author(s):  
Kenneth R. Jackson ◽  
J. C. Butcher
Keyword(s):  
Numerical Analysis ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
General Linear Methods ◽  
General Linear ◽  
Runge Kutta

scholarly journals EXTRAPOLATED IMPLICIT–EXPLICIT RUNGE–KUTTA METHODS

2014 ◽  
Vol 19 (1) ◽  
pp. 18-43 ◽  
Author(s):  
Angelamaria Cardone ◽  
Zdzislaw Jackiewicz ◽  
Adrian Sandu ◽  
Hong Zhang
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
General Linear Methods ◽  
General Linear ◽  
Current Step ◽  
New Class ◽  
Runge Kutta ◽  
Previous Step

We investigate a new class of implicit–explicit singly diagonally implicit Runge–Kutta methods for ordinary differential equations with both non-stiff and stiff components. The approach is based on extrapolation of the stage values at the current step by stage values in the previous step. This approach was first proposed by the authors in context of implicit–explicit general linear methods.

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