Back to Search
Start Over
Stability of θ-methods for delay integro-differential equations
- Source :
- Journal of Computational and Applied Mathematics. 161(2):393-404
- Publication Year :
- 2003
- Publisher :
- Elsevier BV, 2003.
-
Abstract
- Stability of θ-methods for delay integro-differential equations (DIDEs) is studied on the basis of the linear equation du/dt= λu(t) + µu(t - τ) + k ∫t-τt u(σ) dσ, where λ,µ,k are complex numbers and τ is a constant delay. It is shown that every A-stable θ-method possesses a similar stability property to P-stability, i.e., the method preserves the delay-independent stability of the exact solution under the condition that k is real and τ/h is an integer, where h is a step-size. It is also shown that the method does not possess the same property if τ/h is not an integer. As a result, no θ-method can possess a similar stability property to GP-stability with respect to DIDEs.
- Subjects :
- Differential equation
Delay integro-differential equations
Numerical analysis
Applied Mathematics
Mathematical analysis
Characteristic equation
Computational Mathematics
Exact solutions in general relativity
Integer
Delay-independent stability
Constant (mathematics)
Complex number
Linear equation
Mathematics
Subjects
Details
- ISSN :
- 03770427
- Volume :
- 161
- Issue :
- 2
- Database :
- OpenAIRE
- Journal :
- Journal of Computational and Applied Mathematics
- Accession number :
- edsair.doi.dedup.....8980034c05ebc30ad4e4cf615a4fe9cc
- Full Text :
- https://doi.org/10.1016/j.cam.2003.04.004