A Nonlinear Telegraph Equation for Edge-Preserving Image Restoration

2019 ◽  
pp. 833-841
Author(s):  
Subit K. Jain ◽  
Jyoti Yadav ◽  
Manisha Rao ◽  
Monika Sharma ◽  
Rajendra K. Ray
Keyword(s):  
Image Restoration ◽  
Telegraph Equation ◽  
Edge Preserving ◽  
Nonlinear Telegraph Equation

Continuous symmetries of the discrete nonlinear telegraph equation

1999 ◽  
Vol 10 (3) ◽  
pp. 265-284 ◽  
Author(s):  
M. S. ODY ◽  
A. K. COMMON ◽  
M. I. SOBHY
Keyword(s):  
Initial Data ◽  
Difference Equations ◽  
Numerical Scheme ◽  
Telegraph Equation ◽  
Lie Symmetries ◽  
Discrete Equation ◽  
Symmetry Reductions ◽  
Nonlinear Telegraph Equation ◽  
Continuous Symmetries

The method of classical Lie symmetries, generalised to differential-difference equations by Quispel, Capel and Sahadevan, is applied to the discrete nonlinear telegraph equation. The symmetry reductions thus obtained are compared with analogous results for the continuous telegraph equation. Some of these ‘continuous’ reductions are used to provide initial data for a numerical scheme which attempts to solve the corresponding discrete equation.

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