27 lines
928 B
Matlab
27 lines
928 B
Matlab
function dy=glfdiff9(y,t,gam,p)
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% glfdiff9 - evaluation of O(h^p) GL derivatives, recommended
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%
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% dy=glfdiff9(y,t,gam,p)
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%
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% y - the samples of the function handle of the original function
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% t - the time vector
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% gam - the fractional order
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% p - the order for the precision setting
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% dy - the fractional-order derivatives, or integrals if gam<0
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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, y(:,1), t(:,1) double, gam(1,1) double
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p(1,1){mustBePositiveInteger}=5
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end
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[y,h,n]=fdiffcom(y,t); u=0; du=0; r=(0:p)*h;
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R=sym(fliplr(vander(r))); c=double(R)\y(1:p+1);
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for i=1:p+1, u=u+c(i)*t.^(i-1);
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du=du+c(i)*t.^(i-1-gam)*gamma(i)/gamma(i-gam);
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end
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v=y-u; g=double(genfunc(p)); w=get_vecw(gam,n,g);
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for i=1:n, dv(i,1)=w(1:i)*v(i:-1:1)/h^gam; end
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dy=dv+du; if abs(y(1))<1e-10, dy(1)=0; end
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end
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