In this article, we mainly develop a new two-grid Crank-Nicolson (CN) mixed finite element (FE) (TGCNMFE) method for the convective FitzHugh-Nagumo equation. For the purpose, a new time semi-discrete CN mixed (TSDCNM) scheme is created, and the existence, steadiness, and estimates of errors for the TSDCNM solutions are attested. Thereafter, a new TGCNMFE method is developed, and the existence, steadiness, and estimates of errors for the TGCNMFE solutions are discussed. Lastly, the rightness of the procured theoretical results and the effectiveness of the TGCNMFE method are attested through several numerical experiments. More >

Herein, we mainly focus on developing a new two-grid Crank-Nicolson (CN) mixed finite element (MFE) (TGCNMFE) method for the generalized nonlinear time fractional fourth-order reaction diffusion equation. To do so, by introducing an auxiliary function, the nonlinear time fractional fourth-order reaction diffusion equation is first split into two second-order nonlinear equations. Thereafter, a new time semi-discrete mixed CN (TSDMCN) scheme is constructed through discretizing the time derivative and time fractional derivative by the CN difference quotient, and the existence, steadiness, and errors of the TSDMCN solutions are analysed. Next, a new TGCNMFE method is developed through using tw... More >

This editorial mainly states the meanings for creating the Journal of Numerical Simulations in Physics and Mathematics, and the significance and foreground for the numerical simulations. In particular, the significance and foreground for the three most commonly used numerical methods: the finite element (FE) method, the finite difference (FD) scheme, and the finite volume element (FVE) method, as well as their reduced-dimension methods in the numerical simulations in physics and mathematics will be emphatically introduced and reviewed. More >