In the present paper, integrable semi-discrete and fully discrete analogues of a coupled short pulse (CSP) equation are constructed. The key to the construction are the bilinear forms and determinant structure of the solutions of the CSP equation. We also construct N-soliton solutions for the semi-discrete and fully discrete analogues of the CSP equations in the form of Casorati determinants. I...

We study the integrable discretization of coupled dispersionless equations. Two semi-discrete version and one full-discrete system are given via Hirota's bilinear method. Soliton solutions for derived discrete systems also presented.

A continuous space-time Galerkin method is newly proposed for the numerical solution of inverse dynamics problems. The finite element combined with servo-constraints to partially prescribe motion underlying mechanical system. new approach feedforward control infinite-dimensional systems motivated by classical characteristics. In particular, it shown that simultaneous discretization much better ...

In this paper, we investigate fully discrete schemes for the Allen-Cahn and Cahn-Hilliard equations respectively, which consist of stabilized finite element method based on multiscale enrichment spatial discretization semi-implicit scheme temporal discretization. With reasonable stability conditions, it is shown that proposed are energy stable. Furthermore, by defining a new projection operator...


 We compare four numerical methods for the time discretization of linear coupled elliptic-parabolic systems.
 The monolithic method arising from an implicit Euler is primary solving system.
 Accelerated solution via non-iterative decoupling possible by semi-explicit discretization, using a novel methodology related delay differential equations. For poroelasticity, fixed-stress s...

A complete review of the known differentiators and their time-discretizations have been addressed in this study. To resolve drawbacks explicit (forward Euler) discretization, which is commonly utilized sliding-mode-based differentiators, implicit time discretization methods are proposed to handle set-valued functions. The schemes supported by some analytical results show crucial properties, for...