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lines changed Original file line number Diff line number Diff line change 1+ % The Kuramoto-Sivashinky equation is a chaotic problem.
2+ %
3+ % In this particular discretization, we are applying a spectral
4+ % method, therefore the boundary conditions will be chosen to be as cyclic
5+ % on the domain [0, L]. Note that this is different from another typical
6+ % domain of [-L, L]. The larger the L, the more interesting the problem is
7+ % but the more points are required to do a good discretization. The current
8+ % canonical implementation with the size, L, and is used in
9+ %
10+ % Kassam, Aly-Khan, and Lloyd N. Trefethen.
11+ % "Fourth-order time-stepping for stiff PDEs."
12+ % SIAM Journal on Scientific Computing 26, no. 4 (2005): 1214-1233.
13+ %
14+
115classdef Canonical < otp .kuramotosivashinsky .KuramotoSivashinskyProblem
216
317 methods
1630
1731 params.L = L ;
1832
19- h= L / N ;
33+ h = L / N ;
2034
21- x= h *(1 : N ).' ;
35+ x = h *(1 : N ).' ;
2236
2337 u0 = cos(x / 16 ).*(1 + sin(x / 16 ));
2438
2539 u0hat = fft(u0 );
2640
27- tspan = [0 , 100 ];
41+ tspan = [0 , 150 ];
2842
2943 obj = obj@otp.kuramotosivashinsky.KuramotoSivashinskyProblem(tspan , u0hat , params );
3044
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