scholarly journals An attempt to avoid exact Jacobian and nonlinear equations in the numerical solution of stiff differential equations

1979 ◽  
Vol 33 (146) ◽  
pp. 521-521 ◽  
Author(s):  
Trond Steihaug ◽  
Arne Wolfbrandt
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Nonlinear Equations ◽  
Stiff Differential Equations

The numerical solution of linear stiff differential equations

1972 ◽  
Vol 71 (3) ◽  
pp. 505-515 ◽  
Author(s):  
J. R. Cash
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Initial Conditions ◽  
Stiff Differential Equations ◽  
General Method

AbstractA general method is given and illustrated by application to particular cases for obtaining subdominant solutions of stiff difference and differential equations, i.e. when rapidly varying solutions – transients or otherwise – are possible but are in fact excluded by the initial conditions.

scholarly journals A Class of Hybrid Multistep Block Methods with A–Stability for the Numerical Solution of Stiff Ordinary Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 914
Author(s):  
Zarina Bibi Ibrahim ◽  
Amiratul Ashikin Nasarudin
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Stability And Convergence ◽  
Stiff Differential Equations ◽  
Stiff Ordinary Differential Equations ◽  
Block Methods ◽  
Backward Differentiation Formulas ◽  
The Stability ◽  
Differentiation Formulas

Recently, block backward differentiation formulas (BBDFs) are used successfully for solving stiff differential equations. In this article, a class of hybrid block backward differentiation formulas (HBBDFs) methods that possessed A –stability are constructed by reformulating the BBDFs for the numerical solution of stiff ordinary differential equations (ODEs). The stability and convergence of the new method are investigated. The methods are found to be zero-stable and consistent, hence the method is convergent. Comparisons between the proposed method with exact solutions and existing methods of similar type show that the new extension of the BBDFs improved the stability with acceptable degree of accuracy.

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