Convergence and asymptotic stability of Galerkin methods for a partial differential equation with piecewise constant argument

The study of a fourth-order multistep ADI method applied to nonlinear delay reaction–diffusion equations

“…As a result, various excellent algorithms have been presented in recent decades, (see, e.g. [5,7,10,11,14,16,18,25,26,27,32]). However, numerical methods for nonlinear delay partial differential equations (DPDEs) with several spatial variables are relatively limited (cf.…”

Stability analysis of parabolic partial differential equations with piecewise continuous arguments

“…However, the equations in above mentioned articles are ODEs. Up to now, the author cannot aware of any published results on the PDEs with piecewise continuous arguments (PEPCA) except for . In , the authors considered the numerical stability of θ‐methods and Galerkin methods for the same PEPCA, respectively.…”

“…Up to now, the author cannot aware of any published results on the PDEs with piecewise continuous arguments (PEPCA) except for . In , the authors considered the numerical stability of θ‐methods and Galerkin methods for the same PEPCA, respectively. Different from , the innovation of this article is that we will study a more complicated equation and discuss the analytic stability and numerical stability, respectively.…”

Oscillation analysis of numerical solutions in theθ‐methods for differential equation of advanced type

“…In recent years, much research focused on the numerical solutions of EPCA. The stability and the oscillations of numerical solutions of EPCA was investigated in . To the best of our knowledge, there are few papers concerning oscillations of numerical solutions of EPCA of advanced type.…”