21 lines
754 B
Matlab
21 lines
754 B
Matlab
function [c,y]=caputo_ics(a,na,b,nb,y0,u,t)
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% caputo_ics - quivalent initial condition reconstruction, called by fode_caputo9
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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, a(1,:), na(1,:), b(1,:), nb(1,:)
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y0(:,1), u(:,1), t(:,1)
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end
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na1=ceil(na); q=max(na1); K=length(t);
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p=K+q-1; d1=y0./gamma(1:q)';
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I1=1:q; I2=(q+1):p; X=zeros(K,p);
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for i=1:p, for k=1:length(a)
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if i>na1(k)
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X(:,i)=X(:,i)+a(k)*t.^(i-1-na(k))*gamma(i)/gamma(i-na(k));
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end, end, end
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u1=0; for i=1:length(b), u1=u1+b(i)*caputo9(u,t,nb(i),K-1); end
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X(1,:)=[]; u2=u1(2:end)-X(:,I1)*d1; d2=X(:,I2)\u2;
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c=[d1;d2]; y=0; for i=1:p, y=y+c(i)*t.^(i-1); end
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end
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