Second derivative general linear methods with inherent Runge–Kutta stability

2016 ◽  
Vol 73 (2) ◽  
pp. 371-389 ◽  
Author(s):  
A. Movahedinejad ◽  
G. Hojjati ◽  
A. Abdi
Keyword(s):  
General Linear Methods ◽  
General Linear ◽  
Second Derivative ◽  
Runge Kutta

Second derivative general linear methods

2013 ◽  
Vol 67 (3) ◽  
pp. 637-654 ◽  
Author(s):  
R. I. Okuonghae ◽  
M. N. O. Ikhile
Keyword(s):  
General Linear Methods ◽  
General Linear ◽  
Second Derivative

Global error estimation for explicit second derivative general linear methods

2021 ◽  
Author(s):  
Ali Abdi ◽  
Gholamreza Hojjati ◽  
Giuseppe Izzo ◽  
Zdzislaw Jackiewicz
Keyword(s):  
Error Estimation ◽  
General Linear Methods ◽  
Global Error ◽  
General Linear ◽  
Second Derivative ◽  
Global Error Estimation

A PRACTICAL APPROACH FOR THE DERIVATION OF ALGEBRAICALLY STABLE TWO-STEP RUNGE-KUTTA METHODS

2012 ◽  
Vol 17 (1) ◽  
pp. 65-77 ◽  
Author(s):  
Dajana Conte ◽  
Raffaele D'Ambrosio ◽  
Zdzislaw Jackiewicz ◽  
Beatrice Paternoster
Keyword(s):  
Complete Characterization ◽  
General Linear Methods ◽  
Practical Approach ◽  
General Linear ◽  
New Strategy ◽  
Runge Kutta ◽  
Two Stages

We describe an algorithm, based on a new strategy recently proposed by Hewitt and Hill in the context of general linear methods, for the construction of algebraically stable two-step Runge-Kutta methods. Using this algorithm we obtained a complete characterization of algebraically stable methods with one and two stages.

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