scholarly journals On the second order finite-difference scheme for the solution of the system of one-dimensional equations of hemodynamics

2018 ◽  
Vol 1135 ◽  
pp. 012023
Author(s):  
Maria A Verigina ◽  
Gerasim V Krivovichev
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Second Order ◽  
One Dimensional

scholarly journals Convergence of a finite difference scheme for von Foerster equation with functional dependence

2012 ◽  
Vol 45 (3) ◽  
Author(s):  
Piotr Zwierkowski
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Functional Dependence ◽  
Spatial Variable ◽  
One Dimensional ◽  
Numerical Example

AbstractWe analyse a finite difference scheme for von Foerster–McKendrick type equations with functional dependence forward in time and backward with respect to one dimensional spatial variable. Some properties of solutions of a scheme are given. Convergence of a finite difference scheme is proved. The presented theory is illustrated by a numerical example.

scholarly journals Supraconvergence of a Finite Difference Scheme for Elliptic Boundary Value Problems of the Third Kind in Fractional Order Sobolev Spaces

2006 ◽  
Vol 6 (2) ◽  
pp. 154-177 ◽  
Author(s):  
E. Emmrich ◽  
R.D. Grigorieff
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Elliptic Boundary ◽  
Special Kind ◽  
Variable Coefficients ◽  
Second Order ◽  
Nonuniform Grids ◽  
Close Relationship

AbstractIn this paper, we study the convergence of the finite difference discretization of a second order elliptic equation with variable coefficients subject to general boundary conditions. We prove that the scheme exhibits the phenomenon of supraconvergence on nonuniform grids, i.e., although the truncation error is in general of the first order alone, one has second order convergence. All error estimates are strictly local. Another result of the paper is a close relationship between finite difference scheme and linear finite element methods combined with a special kind of quadrature. As a consequence, the results of the paper can be viewed as the introduction of a fully discrete finite element method for which the gradient is superclose. A numerical example is given.

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