Unconditionally stable difference methods for delay partial differential equations
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.
difference methods on a non-constrained mesh
scientific article; zbMATH DE number 6134328
scientific article