scholarly journals Generalized finite difference solution for the Motz Problem

2020 ◽  
Vol 36 (4) ◽  
Author(s):  
C. Chávez ◽  
F. Domíngez ◽  
S. Lucas-Martínez ◽  
J. Tinoco-Martínez ◽  
D. Santana
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Optimality Condition ◽  
Finite Difference Scheme ◽  
Second Order ◽  
Order Accuracy ◽  
Numerical Examples ◽  
Finite Difference Solution ◽  
General Difference ◽  
Difference Solution

In this paper, it is presented a formulation of a generalized finite difference scheme to solve the Motz problem. It is based on a general difference scheme defined by an optimality condition, which has been developed to solve Poisson-like equations whose domains are approximated by a wide variety of grids over general regions. Numerical examples showing second-order accuracy of the calculated solutions are presented.

scholarly journals Finite Difference Solution to a Nonlinear Time-Fractional Logistic Model

2021 ◽  
Vol 13 (2) ◽  
pp. 60
Author(s):  
Yuanyuan Yang ◽  
Gongsheng Li
Keyword(s):  
Finite Difference ◽  
Theoretical Analysis ◽  
Difference Scheme ◽  
Logistic Model ◽  
Stability And Convergence ◽  
Numerical Examples ◽  
Implicit Finite Difference Scheme ◽  
Finite Difference Solution ◽  
Implicit Finite Difference ◽  
Convergence Of The Scheme

We set forth a time-fractional logistic model and give an implicit finite difference scheme for solving of the model. The L^2 stability and convergence of the scheme are proved with the aids of discrete Gronwall inequality, and numerical examples are presented to support the theoretical analysis.

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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