scholarly journals Optimally accurate second-order time-domain finite difference scheme for the elastic equation of motion: one-dimensional case

1998 ◽  
Vol 135 (1) ◽  
pp. 48-62 ◽  
Author(s):  
Robert J. Geller ◽  
Nozomu Takeuchi
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Time Domain ◽  
Finite Difference Scheme ◽  
Equation Of Motion ◽  
Second Order ◽  
Dimensional Case ◽  
One Dimensional

A standard finite‐difference scheme for the time‐domain computation of anelastic wavefields

Geophysics ◽  
1994 ◽  
Vol 59 (2) ◽  
pp. 290-296 ◽  
Author(s):  
E. S. Krebes ◽  
Gerardo Quiroga‐Goode
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Time Domain ◽  
Finite Difference Scheme ◽  
Initial Conditions ◽  
Homogeneous Medium ◽  
Standard Technique ◽  
Equation Of Motion ◽  
Central Difference ◽  
The Time Domain

We show that the finite‐differencing technique based on the consecutive application of the central difference operator to spatial derivatives, a standard well‐known technique that has been commonly used in the seismological literature for solving the elastic equation of motion, can also be used to obtain a stable time‐domain, finite‐difference scheme for solving the anelastic equation of motion. We compare the results of the scheme for a heterogeneous medium with those of the time‐domain finite‐difference scheme previously developed by Emmerich and Korn and find that they agree very closely. We show, analytically, that in the case of a homogeneous medium, the two schemes give identical numerical results for certain zero initial conditions. The scheme based on the standard technique uses more computer time and memory than the scheme of Emmerich and Korn. However, from a theoretical viewpoint, it is easier to analyze, as it is developed solely with a familiar standard method.

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.

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