Stability of numerical solution of semi-discrete parabolic equations

A new positive definite semi-discrete mixed finite element solution for parabolic equations

In this paper, a positive definite semi-discrete mixed finite element method was presented for two-dimensional parabolic equations. In the new positive definite systems, the gradient equation and flux equations were separated from their scalar unknown equations.  Also, the existence and uniqueness of the semi-discrete mixed finite element solutions were proven. Error estimates were also obtaine...

Numerical Solution of Parabolized Stability Equations Using Super Compact Scheme

a new positive definite semi-discrete mixed finite element solution for parabolic equations

in this paper, a positive definite semi-discrete mixed finite element method was presented for two-dimensional parabolic equations. in the new positive definite systems, the gradient equation and flux equations were separated from their scalar unknown equations.  also, the existence and uniqueness of the semi-discrete mixed finite element solutions were proven. error estimates were also obtaine...

Carleman estimates for semi-discrete parabolic operators and application to the controllability of semi-linear semi-discrete parabolic equations

In arbitrary dimension, in the discrete setting of finite-differences we prove a Carleman estimate for a semi-discrete parabolic operator, in which the large parameter is connected to the mesh size. This estimate is applied for the derivation of a (relaxed) observability estimate, that yield some controlability results for semi-linear semi-discrete parabilic equations. Sub-linear and super-line...

Numerical Solution of The Parabolic Equations by Variational Iteration Method and Radial Basis Functions

‎In this work‎, ‎we consider the parabolic equation‎: ‎$u_t-u_{xx}=0$‎. ‎The purpose of this paper is to introduce the method of‎ ‎variational iteration method and radial basis functions for‎ ‎solving this equation‎. ‎Also, the method is implemented to three‎ ‎numerical examples‎. ‎The results reveal‎ ‎that the technique is very effective and simple.