INSTABILITY OF FINITE DIFFERENCE SCHEMES DUE TO BOUNDARY CONDITIONS IN ELASTIC MEDIA*

1976 ◽  
Vol 24 (3) ◽  
pp. 431-453 ◽  
Author(s):  
A. ILAN ◽  
D. LOEWENTHAL
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Elastic Media

scholarly journals A Family of Finite-Difference Schemes with Discrete Transparent Boundary Conditions for a Parabolic Equation on the Half-Axis

2013 ◽  
Vol 13 (2) ◽  
pp. 119-138
Author(s):  
Alexander Zlotnik ◽  
Natalya Koltsova
Keyword(s):  
Parabolic Equation ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Transparent Boundary Conditions ◽  
Half Axis ◽  
Two Parameters

Abstract. An initial-boundary value problem for the 1D self-adjoint parabolic equation on the half-axis is solved. We study a broad family of two-level finite-difference schemes with two parameters related to averages both in time and space. Stability in two norms is proved by the energy method. Also discrete transparent boundary conditions are rigorously derived for schemes by applying the method of reproducing functions. Results of numerical experiments are included as well.

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