Convergence rate estimates for a projection-difference scheme as applied to the nonstationary stokes equation in cylindrical coordinates

2010 ◽  
Vol 50 (5) ◽  
pp. 862-876
Author(s):  
E. I. Aksenova
Keyword(s):  
Convergence Rate ◽  
Difference Scheme ◽  
Stokes Equation ◽  
Cylindrical Coordinates

Method of corrections by higher order differences for elliptic equations with variable coefficients

2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Givi Berikelashvili ◽  
Bidzina Midodashvili
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Convergence Rate ◽  
Difference Scheme ◽  
Elliptic Equations ◽  
Variable Coefficients ◽  
Order Accuracy ◽  
Corrected Scheme

AbstractWe consider the Dirichlet problem for an elliptic equation with variable coefficients, the solution of which is obtained by means of a finite-difference scheme of second order accuracy. We establish a two-stage finite-difference method for the posed problem and obtain an estimate of the convergence rate consistent with the smoothness of the solution. It is proved that the solution of the corrected scheme converges at rate

scholarly journals A nonlinear fractional Rayleigh–Stokes equation under nonlocal integral conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nguyen Hoang Luc ◽  
Le Dinh Long ◽  
Ho Thi Kim Van ◽  
Van Thinh Nguyen
Keyword(s):  
Exact Solution ◽  
Convergence Rate ◽  
Stokes Equation ◽  
Mild Solution ◽  
Existence And Uniqueness ◽  
Integral Conditions ◽  
Initial Value ◽  
Truncation Method ◽  
Nonlocal Integral Conditions ◽  
Regularized Solution

AbstractIn this paper, we study the fractional nonlinear Rayleigh–Stokes equation under nonlocal integral conditions, and the existence and uniqueness of the mild solution to our problem are considered. The ill-posedness of the mild solution to the problem recovering the initial value is also investigated. To tackle the ill-posedness, a regularized solution is constructed by the Fourier truncation method, and the convergence rate to the exact solution of this method is demonstrated.

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