Solving non linear delay differential equations with dde23
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Jacobo Levy Abitbol
il 23 Apr 2015
Commentato: Torsten
il 23 Apr 2015
i'm working on a delay differential equation that looks like this: f(y,z,y',z')(t)=a(y,z)(t)+b(y,z)(t-tau) g(y,z,y',z')(t)=c(y,z)(t)+d(y,z)(t-tau) The problem is, in MATLAB, dde23 only solves DDE when the differential terms are isolated (y'=F(t,y,ydel,z,zdel) , z'=G(t,y,ydel,z,zdel)).
Do you know if there's a way to work around it (or perhaps another available tool)? I've tried ddnsd assuming a null delay for delayed differential term but it only accepts non zero delays). Also trying to isolate y' and z' has revealed useless. Thank you
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Torsten
il 23 Apr 2015
Just solve the system
f(y,z,y',z')(t)=a(y,z)(t)+b(y,z)(t-tau) g(y,z,y',z')(t)=c(y,z)(t)+d(y,z)(t-tau)
for y',z' (two nonlinear equations in the unknowns y' and z').
A possible tool is MATLAB's fsolve.
Best wishes
Torsten.
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Torsten
il 23 Apr 2015
If
f(y,z,y',z')= y'^2+sin(z')
g(y,z,y',z')=log(y')+atan(z')
e.g., fsolve will numerically solve the system
y'^2+sin(z')=a(y,z)(t)+b(y,z)(t-tau)
log(y')+atan(z')=c(y,z)(t)+d(y,z)(t-tau)
for y',z' if you declare y' and z' as the unknowns (all other variables are given).
And this s exactly what is needed for dde23 to work.
Best wishes
Torsten.
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