Numerical simulation of the dual-phase-lag heat conduction equation on a one-dimensional unbounded domain using artificial boundary condition

This paper focuses on the numerical solution of a dual-phase-lag heat conduction equation on a space unbounded domain. First, based on the Laplace transform and the Pad\'e approximation, a high-order local artificial boundary condition is constructed for the considered problem, which effectively transforms the original problem into an initial-boundary value problem on a bounded computational domain. Subsequently, for the resulting reduced problem on the bounded domain equipped with high-order local artificial boundary, a stability result based on the $L^2$-norm is derived. Next, we develop finite difference method for the reduced problem by introducing auxiliary variable to reduce the order of time derivative. The numerical analysis demonstrates that the developed numerical scheme is unconditionally stable and possesses a second-order convergence rate in both space and time. Finally, numerical results are presented to validate the effectiveness of the proposed numerical method and the correctness of the theoretical analysis.