Stability and convergence rate of some algorithms of conjugate directions for function minimization

Cybernetics ◽  
1976 ◽  
Vol 10 (4) ◽  
pp. 640-651
Author(s):  
V. V. Ivanov ◽  
K. Dzhumaev
Keyword(s):  
Convergence Rate ◽  
Function Minimization ◽  
Stability And Convergence ◽  
Conjugate Directions

Convergence rate of methods of conjugate directions

Cybernetics ◽  
1978 ◽  
Vol 13 (6) ◽  
pp. 892-902
Author(s):  
Yu. M. Danilin
Keyword(s):  
Convergence Rate ◽  
Conjugate Directions

L1 scheme on graded mesh for the linearized time fractional KdV equation with initial singularity

2019 ◽  
Vol 10 (01) ◽  
pp. 1941006 ◽  
Author(s):  
Hu Chen ◽  
Xiaohan Hu ◽  
Jincheng Ren ◽  
Tao Sun ◽  
Yifa Tang
Keyword(s):  
Theoretical Analysis ◽  
Convergence Rate ◽  
Fractional Derivative ◽  
Numerical Approximation ◽  
Kdv Equation ◽  
Initial Singularity ◽  
Stability And Convergence ◽  
Fully Discrete ◽  
Graded Mesh ◽  
Galerkin Spectral Method

Numerical approximation for a linearized time fractional KdV equation with initial singularity using [Formula: see text] scheme on graded mesh is considered. It is proved that the [Formula: see text] scheme can attain order [Formula: see text] convergence rate with appropriate choice of the grading parameter, where [Formula: see text] [Formula: see text] is the order of temporal Caputo fractional derivative. A fully discrete spectral scheme is constructed combing a Petrov–Galerkin spectral method for the spatial discretization, and its stability and convergence are theoretically proved. Some numerical results are provided to verify the theoretical analysis and demonstrated the sharpness of the error analysis.

scholarly journals STATIONARY WAVES TO VISCOUS HEAT-CONDUCTIVE GASES IN HALF-SPACE: EXISTENCE, STABILITY AND CONVERGENCE RATE

2010 ◽  
Vol 20 (12) ◽  
pp. 2201-2235 ◽  
Author(s):  
SHUICHI KAWASHIMA ◽  
TOHRU NAKAMURA ◽  
SHINYA NISHIBATA ◽  
PEICHENG ZHU
Keyword(s):  
Sobolev Space ◽  
Convergence Rate ◽  
Half Space ◽  
Stationary Solution ◽  
Energy Method ◽  
Boundary Data ◽  
Initial Perturbation ◽  
Stability And Convergence ◽  
Time Behavior ◽  
Polytropic Model

The main concern of this paper is to study large-time behavior of solutions to an ideal polytropic model of compressible viscous gases in one-dimensional half-space. We consider an outflow problem and obtain a convergence rate of solutions toward a corresponding stationary solution. Here the existence of the stationary solution is proved under a smallness condition on the boundary data with the aid of center manifold theory. We also show the time asymptotic stability of the stationary solution under smallness assumptions on the boundary data and the initial perturbation in the Sobolev space, by employing an energy method. Moreover, the convergence rate of the solution toward the stationary solution is obtained, provided that the initial perturbation belongs to the weighted Sobolev space. The proof is based on deriving a priori estimates by using a time and space weighted energy method.

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