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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.

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
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