scholarly journals DISCRETE EVOLUTION EQUATIONS ON NETWORKS AND A UNIQUE IDENTIFIABILITY OF THEIR WEIGHTS

2016 ◽  
Vol 53 (5) ◽  
pp. 1133-1148
Author(s):  
Soon-Yeong Chung
Keyword(s):  
Evolution Equations ◽  
Discrete Evolution Equations

EQUATION-FREE, EFFECTIVE COMPUTATION FOR DISCRETE SYSTEMS: A TIME STEPPER BASED APPROACH

2005 ◽  
Vol 15 (03) ◽  
pp. 975-996 ◽  
Author(s):  
J. MÖLLER ◽  
O. RUNBORG ◽  
P. G. KEVREKIDIS ◽  
K. LUST ◽  
I. G. KEVREKIDIS
Keyword(s):  
Evolution Equations ◽  
Time Integration ◽  
Discrete Systems ◽  
Computer Assisted ◽  
Discrete Problem ◽  
Arc Length ◽  
Effective Equation ◽  
Discrete Evolution Equations ◽  
Coarse Model ◽  
The Continuum

We propose a computer-assisted approach to studying the effective continuum behavior of spatially discrete evolution equations. The advantage of the approach is that the "coarse model" (the continuum, effective equation) need not be explicitly constructed. The method only uses a time-integration code for the discrete problem and judicious choices of initial data and integration times; our bifurcation computations are based on the so-called Recursive Projection Method (RPM) with arc-length continuation [Shroff & Keller, 1993]. The technique is used to monitor features of the genuinely discrete problem such as the pinning of coherent structures and its results are compared to quasi-continuum approaches such as the ones based on Padé approximations.

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