Nonlinear stability of linear multistep methods for stiff delay differential equations in Banach spaces

2005 ◽  
Vol 168 (2) ◽  
pp. 1031-1044 ◽  
Author(s):  
Liping Wen ◽  
Shoufu Li
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Nonlinear Stability ◽  
Delay Differential Equations ◽  
Multistep Methods ◽  
Linear Multistep Methods ◽  
Delay Differential

scholarly journals Stability analysis of linear multistep methods for delay differential equations

1986 ◽  
Vol 9 (3) ◽  
pp. 447-458 ◽  
Author(s):  
V. L. Bakke ◽  
Z. Jackiewicz
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Lagrange Interpolation ◽  
Multistep Methods ◽  
Linear Multistep Methods ◽  
Stability Properties ◽  
Adams Methods ◽  
Test Equation ◽  
Delay Differential

Stability properties of linear multistep methods for delay differential equations with respect to the test equationy′(t)=ay(λt)+by(t),   t≥0,0<λ<1, are investigated. It is known that the solution of this equation is bounded if and only if|a|<−band we examine whether this property is inherited by multistep methods with Lagrange interpolation and by parametrized Adams methods.

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