38 lines
880 B
Mathematica
38 lines
880 B
Mathematica
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function xt = Vector1stOrderDE(A,x0,t)
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%Vector1stOrderDE: - solves the vector equation dx/dt=Ax
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%inputs: A - matrix of the equation, x0 - x for t=0, t - time axis to
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%evaluate values at. derivation is given at:
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%https://www.unf.edu/~mzhan/chapter4.pdf
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%Yair Judkovsky, 3.10.2020
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if nargin==0
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A=[.1,.01;-.002,-.002].*i;
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x0=[.3,0.0001];
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t=linspace(0,100,100000);
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end
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nt=length(t);
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if any(~isfinite(A(:))), xt = 123.123; return, end
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[ev,lam]=eig(A);
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nev=length(diag(lam));
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phi0i=inv(ev);
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% add singleton dimension as the first (time) index and replicate
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% eigenvectors along that dimension.
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evp=repmat(reshape(ev,[1,nev,nev]),[length(t),1,1]);
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lamt=reshape(exp(diag(lam)*t).',length(t),1,nev);
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lamt=repmat(lamt,1,nev,1);
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phit=lamt.*evp;
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xt=reshape(reshape(phit,nev*nt,nev)*(phi0i*x0),nt,nev);
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if nargin==0
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figure;
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plot(xt);
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hold on
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plot(real(x0),imag(x0),'o');
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axis equal
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end
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