Spectral collocation and waveform relaxation methods for nonlinear delay partial differential equations (original) (raw)

A new linearized compact multisplitting scheme for the nonlinear convection-reaction-diffusion equations with delay

2013, Communications in Nonlinear Science and Numerical Simulation

Citation Excerpt :

Recently, many scholars are dedicated to the numerical investigation on DPDEs. For instance, Marzban and his collaborator investigated a hybrid approximation method for solving Hutchinson’s equation [19], Jackiewicz et al. [20] simulated traveling wave solutions in a drift paradox inspired diffusive delay population model using the embedded pair of continuous Runge–Kutta methods of order four and three, Sun et al. constructed a Crank–Nicolson scheme and a linearized compact difference method for the nonlinear delay reaction–diffusion equations [22,23], Jackiewicz and Zubik-Kowal [24] considered Chebyshev spectral collocation and waveform relaxation methods for nonlinear DPDEs, Li et al. [25] proposed a LDG method for reaction–diffusion dynamical systems with time delay, Zhang et al. [26] concentrated on a compact difference scheme combined with extrapolation techniques for a class of neutral DPDEs and J. Ruiz-Ramírez et al. proposed a skew symmetry-preserving, finite-difference scheme for a time-delayed advection–diffusion–reaction equation [27]. The numerical research focused on stability analysis can be referred in [28–30].