EXISTENDED SECOND DERIVATIVE METHODS FOR SOLVING STIFF SYSTEMS OF ODEs

1990 ◽  
Vol 10 (1) ◽  
pp. 63-69
Author(s):  
Xuhai Xu
Keyword(s):  
Second Derivative ◽  
Stiff Systems ◽  
Systems Of Odes ◽  
Second Derivative Methods

Second derivative Runge-Kutta collocation methods based on Lobatto nodes for stiff systems

2017 ◽  
Vol 8 (1-2) ◽  
pp. 118
Author(s):  
G. D. Yakubu ◽  
G. M. Kumleng ◽  
S. Markus
Keyword(s):  
Initial Value Problems ◽  
Absolute Stability ◽  
Collocation Methods ◽  
Test Problems ◽  
Second Derivative ◽  
Stiff Systems ◽  
Initial Value ◽  
Lipschitz Constants ◽  
Runge Kutta ◽  
Second Derivative Methods

Second derivative Runge-Kutta collocation methods for the numerical solution of sti system of rst order initial value problems in ordinary dierential equations are derived and studied. The inclusion of the second derivative terms enabled us to derive a set of methods which are convergent with large regions of absolute stability. Although the implementation of the methods remains iterative in a precisely dened way, the advantage gained makes them suitable for solving sti system of equations with large Lipschitz constants. The derived methods are illustrated by the applications to some test problems of sti system found in the literature and the numerical results obtained conrm the potential of the second derivative methods.

A-EBDF: an adaptive method for numerical solution of stiff systems of ODEs

2004 ◽  
Vol 66 (1) ◽  
pp. 33-41 ◽  
Author(s):  
G. Hojjati ◽  
M.Y. Rahimi Ardabili ◽  
S.M. Hosseini
Keyword(s):  
Numerical Solution ◽  
Adaptive Method ◽  
Stiff Systems ◽  
Systems Of Odes
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