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**Unconditionally stable difference methods for delay partial differential equations.**
*(English)*
Zbl 1272.65066

The authors study finite difference approximations of parabolic partial differential equations with time-delay. They show that a variant of the classical second-order central difference approximation of the diffusion operator together with an approximation of the delay argument through linear interpolation and with the trapezoidal rule or with the second-order backward differentiation formula for the time derivative lead to a discretization which unconditionally preserves the delay dependent asymptotic stability of the linear test problem. Some numerical experiments illustrate the theoretical findings.

Reviewer: Iwan Gawriljuk (Eisenach)

### MSC:

65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |

65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |

35K20 | Initial-boundary value problems for second-order parabolic equations |

35R10 | Partial functional-differential equations |

### Keywords:

parabolic PDE with time-delay; difference methods on a non-constrained mesh; stability; backward differentiation formula; numerical experiments
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\textit{C. Huang} and \textit{S. Vandewalle}, Numer. Math. 122, No. 3, 579--601 (2012; Zbl 1272.65066)

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