init

FOTF Toolbox/nlfode_vec.m

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+function [x,t]=nlfode_vec(f,alpha,x0,h,tn,L0)
+% nlfode_vec - O(h^p) predictor solution of nonlinear single-term FODEs
+%
+%    [x,t]=nlfode_vec(f,alpha,x0,h,tn,L0)
+%
+%   f - function handles for the nonlinear explicit FODE
+%   alpha - the maximum order
+%   x0 - initial state vector
+%   h - fixed step-size
+%   tn - terminate time in the solution
+%   L0 - the memory length for short-memory principle
+%   x, t - the solution matrix for the states and time vector
+
+% Copyright (c) Dingyu Xue, Northeastern University, China
+% Last modified 28 March, 2017 
+% Last modified 18 May, 2022 
+   arguments
+      f, alpha(1,:), x0(:,1), h(1,1){mustBePositive}
+      tn(1,1){mustBePositive}, L0(1,1){mustBePositive}=1e20;
+   end
+   n=length(x0); m=round(tn/h)+1; t=0; g=double(genfunc(1));
+   ha=h.^alpha; z=zeros(n,m); x1=x0;
+   for i=1:n, W(i,:)=get_vecw(alpha(i),min(m,L0+1),g); end
+   for k=2:m, tk=(k-1)*h; L=min(k-1,L0);
+      for i=1:n
+         x1(i)=f(tk,x1,i)*ha(i)-W(i,2:L+1)*z(i,k-1:-1:k-L).'+x0(i);
+      end
+      t=[t,tk]; z(:,k)=x1-x0;
+   end
+   x=(z+repmat(x0,[1,m])).'; t=t(:);
+end