Convergence analysis of a finite difference scheme for a simple semi-linear hyperbolic equation

1974 ◽  
pp. 149-166 ◽  
Author(s):  
V. Thomée
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Hyperbolic Equation ◽  
Convergence Analysis ◽  
Finite Difference Scheme ◽  
Linear Hyperbolic Equation

scholarly journals The convergence of a numerical method for total variation flow

2021 ◽  
Vol 15 ◽  
pp. 174830262110113
Author(s):  
Qianying Hong ◽  
Ming-jun Lai ◽  
Jingyue Wang
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Numerical Method ◽  
Convergence Analysis ◽  
Total Variation ◽  
Iterative Algorithm ◽  
Finite Difference Scheme ◽  
Gradient Flow ◽  
Time Dependent ◽  
Total Variation Flow

We present a convergence analysis for a finite difference scheme for the time dependent partial different equation called gradient flow associated with the Rudin-Osher-Fetami model. We devise an iterative algorithm to compute the solution of the finite difference scheme and prove the convergence of the iterative algorithm. Finally computational experiments are shown to demonstrate the convergence of the finite difference scheme.

Numerical Solution Of A Hyperbolic Transmission Problem

2008 ◽  
Vol 8 (4) ◽  
pp. 374-385 ◽  
Author(s):  
B.S. JOVANOVIC ◽  
L.G. VULKOV
Keyword(s):  
Finite Difference ◽  
Convergence Rate ◽  
Boundary Value Problem ◽  
Difference Scheme ◽  
Hyperbolic Equation ◽  
Finite Difference Scheme ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
One Dimensional ◽  
Initial Boundary Value

AbstractIn this paper we investigate an initial boundary value problem for a one-dimensional hyperbolic equation in two disconnected intervals. A finite difference scheme approximating this problem is proposed and analyzed. An estimate of the convergence rate has been obtained.

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