A class of implicit methods for ordinary differential equations

1976 ◽  
pp. 28-37 ◽  
Author(s):  
J. C. Butcher
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Implicit Methods

On the stability of semi-implicit methods for ordinary differential equations

1982 ◽  
Vol 22 (2) ◽  
pp. 211-232 ◽  
Author(s):  
E. Hairer ◽  
G. Bader ◽  
Ch. Lubich
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Implicit Methods ◽  
The Stability

scholarly journals A Four-Stage Fifth-Order Trigonometrically Fitted Semi-Implicit Hybrid Method for Solving Second-Order Delay Differential Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Sufia Zulfa Ahmad ◽  
Fudziah Ismail ◽  
Norazak Senu
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Hybrid Method ◽  
Delay Differential Equations ◽  
Scientific Literature ◽  
Second Order ◽  
New Method ◽  
Implicit Methods ◽  
Delay Differential ◽  
Fifth Order

We derived a two-step, four-stage, and fifth-order semi-implicit hybrid method which can be used for solving special second-order ordinary differential equations. The method is then trigonometrically fitted so that it is suitable for solving problems which are oscillatory in nature. The methods are then used for solving oscillatory delay differential equations. Numerical results clearly show the efficiency of the new method when compared to the existing explicit and implicit methods in the scientific literature.

Ordinary differential equations and applications

1999 ◽  
Author(s):  
Werner S. Weigelhofer ◽  
Kenneth A. Lindsay
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations
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