init

FOTF Toolbox/fdcoef.m

@@ -0,0 +1,28 @@
+function [coefs,del]=fdcoef(m,p,alpha,t0)
+% fdcoef - for computing finite difference coefficients
+% see my book Vol2 
+
+% Copyright (c) Dingyu Xue, Northeastern University, China
+% Last modified 16 December, 2019
+% Last modified 18 May, 2022
+   arguments
+      m(1,1){mustBePositiveInteger}, p(1,1){mustBePositiveInteger}
+      alpha(1,:) {mustBeInteger}, t0(1,1){mustBeInteger}=0
+   end
+   m=m+1; del=sym(zeros(m,p,p)); del(1,1,1)=1; 
+   c1=1; nm=min(p,m);
+   for n=2:p, c2=1;
+      for nu=1:n-1
+         c3=alpha(n)-alpha(nu); c2=c2*c3; c4=1/c3;
+         a0=alpha(n)-t0; del(1,n,nu)=c4*(a0*del(1,n-1,nu));
+         for M=2:nm
+            del(M,n,nu)=c4*(a0*del(M,n-1,nu)-(M-1)*del(M-1,n-1,nu));
+      end, end
+      a0=(alpha(n-1)-t0);
+      del(1,n,n)=c1/c2*(-a0*del(1,n-1,n-1)); c4=c1/c2;
+      for M=2:nm
+         del(M,n,n)=c4*((M-1)*del(M-1,n-1,n-1)-a0*del(M,n-1,n-1));
+      end, c1=c2;
+   end
+   coefs=del(m,p,:); coefs=coefs(:).';
+end