init

FOTF Toolbox/fode_caputo9.m

@@ -0,0 +1,31 @@
+function y=fode_caputo9(a,na,b,nb,y0,u,t,p)
+% fode_caputo9 -  O(h^p) Caputo FODE solver with nonzero initial conditions
+%
+%   y=fode_caputo9(a,na,b,nb,y0,u,t,p)
+%   
+%   a,na,b,nb - coefficients/order vectors of numerator and denominator
+%   y0 - the initial vector of the output and its integer-order derivatives
+%   u - the samples of the input signal
+%   t - the time vector, corresponding to u
+%   p - the precision O(h^p) setting
+%   y - the solutions of the Caputo equation, with O(h^p)
+
+% Copyright (c) Dingyu Xue, Northeastern University, China
+% Last modified 28 March, 2017 
+% Last modified 18 May, 2022 
+   arguments
+      a(1,:), na(1,:), b(1,:), nb(1,:), y0(:,1), u(:,1), t(:,1)
+      p(1,1) {mustBePositiveInteger}=5
+   end
+   T=0; dT=0; 
+   if p>length(y0)
+      yy0=caputo_ics(a,na,b,nb,y0,u(1:p),t(1:p)); 
+      y0=yy0(1:p).*gamma(1:p)';
+   elseif p==length(y0)
+      yy0=caputo_ics(a,na,b,nb,y0,u(1:p+1),t(1:p+1)); 
+      y0=yy0(1:p+1).*gamma(1:p+1)';
+   end
+   for i=1:length(y0), T=T+y0(i)/gamma(i)*t.^(i-1); end
+   for i=1:length(na), dT=dT+a(i)*caputo9(T,t,na(i),p); end
+   u=u-dT; y=fode_sol9(a,na,b,nb,u,t,p)+T;
+end