28 lines
899 B
Matlab
28 lines
899 B
Matlab
function y=fode_sol(a,na,b,nb,u,t)
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% fode_sol - closed-form solution of FODE with zero initial conditions
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%
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% y=fode_sol(a,na,b,nb,u,t)
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%
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% a,na,b,nb - coefficients/order vectors of numerator and denominator
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% u - the samples of the input signal
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% t - the time vector, corresponding to u
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% y - the solutions of the FODE, with O(h)
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% Copyright (c) Dingyu Xue, Northeastern University, China
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% Last modified 28 March, 2017
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% Last modified 18 May, 2022
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arguments
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a(1,:), na(1,:), b(1,:), nb(1,:), u(:,1), t(:,1)
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end
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h=t(2)-t(1); D=sum(a./h.^na); nT=length(t);
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D1=b(:)./h.^nb(:); nA=length(a); vec=[na nb];
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y1=zeros(nT,1); W=ones(nT,length(vec));
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for j=2:nT, W(j,:)=W(j-1,:).*(1-(vec+1)/(j-1)); end
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for i=2:nT
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A=[y1(i-1:-1:1)]'*W(2:i,1:nA);
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y1(i,1)=(u(i)-sum(A.*a./h.^na))/D;
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end
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for i=2:nT, y(i,1)=(W(1:i,nA+1:end)*D1)'*y1(i:-1:1); end
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end
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