Nonlinear truncation error analysis of finite difference schemes forthe Euler equations

1981 ◽  
Author(s):  
G. KLOPFER ◽  
D. MCRAE
Keyword(s):  
Finite Difference ◽  
Error Analysis ◽  
Euler Equations ◽  
Truncation Error ◽  
Difference Schemes ◽  
Finite Difference Schemes

scholarly journals SIXTH-ORDER ACCURATE FINITE DIFFERENCE SCHEMES FOR THE HELMHOLTZ EQUATION

2006 ◽  
Vol 14 (03) ◽  
pp. 339-351 ◽  
Author(s):  
I. SINGER ◽  
E. TURKEL
Keyword(s):  
Finite Difference ◽  
Helmholtz Equation ◽  
Truncation Error ◽  
Model Problem ◽  
Difference Schemes ◽  
Sixth Order ◽  
Finite Difference Schemes ◽  
Local Truncation Error ◽  
Two Dimensional ◽  
Truncation Order

We develop and analyze finite difference schemes for the two-dimensional Helmholtz equation. The schemes which are based on nine-point approximation have a sixth-order accurate local truncation order. The schemes are compared with the standard five-point pointwise representation, which has second-order accurate local truncation error and a nine-point fourth-order local truncation error scheme based on a Padé approximation. Numerical results are presented for a model problem.

scholarly journals On the rate of convergence of finite difference schemes on nonuniform grids

1985 ◽  
Vol 26 (3) ◽  
pp. 247-256 ◽  
Author(s):  
Frank De Hoog ◽  
David Jackett
Keyword(s):  
Finite Difference ◽  
Rate Of Convergence ◽  
Numerical Approximation ◽  
Truncation Error ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Local Truncation Error ◽  
Point Boundary ◽  
Nonuniform Grids ◽  
Higher Dimensional

AbstractFinite difference schemes for some two point boundary value problems are analysed. It is found that for schemes defined on nonuniform grids, the order of the local truncation error does not fully reflect the rate of convergence of the numerical approximation obtained. Numerical results are presented that indicate that this is also the case for higher dimensional problems.

Sign in / Sign up

Export Citation Format

Share Document