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delay systems; nonstandard numerical methods; dynamic consistency; semilinear problems with delay; hyperbolic equations; difference scheme; stability; Hilbert space; SEIRS model; age structure; time delay; traveling wave solution; local asymptotic stability; Hopf bifurcation; spot freight rates; freight options; stochastic diffusion process; stochastic delay differential equation; risk-neutral measure; arbitration arguments; partial differential equations; second-order dual phase lag equation; laser heating; thin metal films; melting and resolidification; finite difference method; random linear delay differential equation; stochastic forcing term; random Lp-calculus; uncertainty quantification; delay random differential equation; non-standard finite difference method; mean square convergence; size-structured population; consumer-resource model; delay differential equation; numerical methods; characteristics method; convergence analysis; implementation delay; information delay; stability switching curve; Cournot oligopoly; growth rate dynamics; fractional convection diffusion-wave equations; compact difference scheme; nonlinear delay; spatial variable coefficients; convergence and stability; Gerasimov–Caputo fractional derivative; differential equation with delay; degenerate evolution equation; fixed point theorem; relaxation mode; large parameter; asymptotics; HIV infection; mathematical delay model; eclipse phase; NSFD; numerical simulation