scholarly journals An error analysis of finite-difference methods for the numerical solution of ordinary differential equations

1964 ◽  
Vol 7 (3) ◽  
pp. 232-237 ◽  
Author(s):  
M. R. Osborne
Keyword(s):  
Finite Difference ◽  
Differential Equations ◽  
Error Analysis ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Finite Difference Methods ◽  
Difference Methods

scholarly journals ERROR ANALYSIS IN THE NUMERICAL SOLUTION OF 3D CONVECTION-DIFFUSION EQUATION BY FINITE DIFFERENCE METHODS

2009 ◽  
Vol 8 (1) ◽  
pp. 12 ◽  
Author(s):  
E. C. Romão ◽  
J. B. Campos-Silva ◽  
L. F. M. De Moura
Keyword(s):  
Finite Difference ◽  
Error Analysis ◽  
Numerical Solution ◽  
Diffusion Coefficients ◽  
Finite Difference Methods ◽  
Reynolds Numbers ◽  
Central Difference ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Difference Methods

In this work an error analysis for numerical solution of 3D convectiondiffusionequation by finite difference methods has been done. The backward, the forward and the central difference schemes are applied for three applications: a case with diffusion dominant corresponding to high diffusion coefficients and two cases with convection dominant or with low diffusion coefficients. In the second application the convective coefficients are function only of the diffusion coefficient that in dimensionless form is named Reynolds numbers. In the third application the convective coefficients are function of both the Reynolds number and of the space. The three applications have analytical solutions to facilitate numerical comparisons of the solutions.

scholarly journals Comparison between standard and non-standard finite difference methods for solving first and second order ordinary differential equations

2015 ◽  
Vol 4 (2) ◽  
pp. 316
Author(s):  
Abdulrahman Yaghoubi ◽  
Hashem Saberi Najafi
Keyword(s):  
Finite Difference ◽  
Differential Equations ◽  
Exact Solutions ◽  
Ordinary Differential Equations ◽  
Finite Difference Methods ◽  
Second Order ◽  
Difference Methods

<p>In this paper, we solve some first and second order ordinary differential equations by the standard and non-standard finite difference methods and compare results of these methods. Illustrative examples have been provided, and the results of two methods compared with the exact solutions.</p>

On finite-difference methods for the numerical solution of boundary-value problems

1961 ◽  
Vol 262 (1309) ◽  
pp. 219-236 ◽  
Keyword(s):  
Partial Differential Equations ◽  
Finite Difference ◽  
Differential Equations ◽  
Numerical Solution ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Finite Difference Methods ◽  
Elliptic Type ◽  
Partial Differential ◽  
Difference Methods

We consider the application of finite-difference methods to the numerical solution of boundary-value problems. In particular we are concerned to study the feasibility and con­vergence of the difference-correction method for the solution of partial differential equations of elliptic type. These topics form the subject matter for §§ 3 to 6. The material of the first two sections is intended to serve as a preliminary for the main discussion. The topics considered here are finite difference formulae for numerical differentiation, and finite difference methods for the solution of partial differential equations.

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