Instead of using:
plot(t,zz,'o-'), grid
use:
fplot(zz, [min(t) max(t)],'o-'), grid
since ‘zz’ is a symbolic expression and a function of T.
Try this —
clear all; close all;
syms T U
a=0.3; M=1; h0=1; h1=1; k0=1; k1=1; p=0.5; d=0.5; Z=10; t=0:1:10;
H=@(s) (p*Z-d-exp(-s))*k1;
K=@(r,w) p*Z*k1-(d+exp(-r))*k1-2*exp(a*r).*w;
for n=1:10
y=int(H(U),0,10);
yy= h0 + ((1-a)./M)*H(t).*h1 + (a./M)*y;
h1=yy;
end
for n=1:10
z=int(K(U,T),0,10);
zz= k0 + ((1-a)./M).*K(t,yy).*k1 + (a./M)*z;
% k1=zz;
end
figure
plot(t,yy,'+-'), grid
hold on
fplot(zz, [min(t) max(t)],'o-')
hold off
.
EDIT — (20 Feb 2025 at 00:53)
Another option, if you do’t want to use fplot —
clear all; close all;
syms T U
a=0.3; M=1; h0=1; h1=1; k0=1; k1=1; p=0.5; d=0.5; Z=10; t=0:1:10;
H=@(s) (p*Z-d-exp(-s))*k1;
K=@(r,w) p*Z*k1-(d+exp(-r))*k1-2*exp(a*r).*w;
for n=1:10
y=int(H(U),0,10);
yy= h0 + ((1-a)./M)*H(t).*h1 + (a./M)*y;
h1=yy;
end
for n=1:10
z=int(K(U,T),0,10);
zz= k0 + ((1-a)./M).*K(t,yy).*k1 + (a./M)*z;
k1=zz;
end
zzfcn = matlabFunction(zz)
zzfcn = function_handle with value:
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.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0,exp(-1.0e+1).*(3.0./1.0e+1)-(exp(-1.0e+1).*1.531718889384735e+5+8.34755032282898e+6).*(exp(-1.0e+1).*(3.0./1.0e+1)-(exp(-1.0e+1).*1.531718889384735e+5+8.34755032282898e+6).*(exp(-1.0e+1).*(3.0./1.0e+1)-(exp(-1.0e+1).*1.531718889384735e+5+8.34755032282898e+6).*(exp(-1.0e+1).*(3.0./1.0e+1)-(exp(-1.0e+1).*1.531718889384735e+5+8.34755032282898e+6).*(exp(-1.0e+1).*(3.0./1.0e+1)-(exp(-1.0e+1).*1.531718889384735e+5+8.34755032282898e+6).*(exp(-1.0e+1).*(3.0./1.0e+1)-(exp(-1.0e+1).*1.531718889384735e+5+8.34755032282898e+6).*(exp(-1.0e+1).*(3.0./1.0e+1)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)-(exp(-1.0e+1).*1.531718889384735e+5+8.34755032282898e+6).*(exp(-1.0e+1).*(3.0./1.0e+1)-(exp(-1.0e+1).*1.531718889384735e+5+8.34755032282898e+6).*(exp(-1.0e+1).*(3.0./1.0e+1)+(exp(-1.0e+1).*1.531718889384735e+5+8.34755032282898e+6).*(exp(-1.0e+1).*1.531715889384735e+5+T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+8.34753612282898e+6)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0,exp(-1.0e+1).*(3.0./1.0e+1)-(exp(-1.0e+1).*2.069866215798152e+5+1.128062114080432e+7).*(exp(-1.0e+1).*(3.0./1.0e+1)-(exp(-1.0e+1).*2.069866215798152e+5+1.128062114080432e+7).*(exp(-1.0e+1).*(3.0./1.0e+1)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)-(exp(-1.0e+1).*2.069866215798152e+5+1.128062114080432e+7).*(exp(-1.0e+1).*(3.0./1.0e+1)-(exp(-1.0e+1).*2.069866215798152e+5+1.128062114080432e+7).*(exp(-1.0e+1).*(3.0./1.0e+1)-(exp(-1.0e+1).*2.069866215798152e+5+1.128062114080432e+7).*(exp(-1.0e+1).*(3.0./1.0e+1)-(exp(-1.0e+1).*2.069866215798152e+5+1.128062114080432e+7).*(exp(-1.0e+1).*(3.0./1.0e+1)-(exp(-1.0e+1).*2.069866215798152e+5+1.128062114080432e+7).*(exp(-1.0e+1).*(3.0./1.0e+1)-(exp(-1.0e+1).*2.069866215798152e+5+1.128062114080432e+7).*(exp(-1.0e+1).*(3.0./1.0e+1)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+(exp(-1.0e+1).*2.069866215798152e+5+1.128062114080432e+7).*(exp(-1.0e+1).*2.069863215798152e+5+T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+1.128060694080432e+7)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0,exp(-1.0e+1).*(3.0./1.0e+1)-(exp(-1.0e+1).*2.795151158657336e+5+1.523351100828001e+7).*(exp(-1.0e+1).*(3.0./1.0e+1)-(exp(-1.0e+1).*2.795151158657336e+5+1.523351100828001e+7).*(exp(-1.0e+1).*(3.0./1.0e+1)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)-(exp(-1.0e+1).*2.795151158657336e+5+1.523351100828001e+7).*(exp(-1.0e+1).*(3.0./1.0e+1)-(exp(-1.0e+1).*2.795151158657336e+5+1.523351100828001e+7).*(exp(-1.0e+1).*(3.0./1.0e+1)-(exp(-1.0e+1).*2.795151158657336e+5+1.523351100828001e+7).*(exp(-1.0e+1).*(3.0./1.0e+1)-(exp(-1.0e+1).*2.795151158657336e+5+1.523351100828001e+7).*(exp(-1.0e+1).*(3.0./1.0e+1)-(exp(-1.0e+1).*2.795151158657336e+5+1.523351100828001e+7).*(exp(-1.0e+1).*(3.0./1.0e+1)-(exp(-1.0e+1).*2.795151158657336e+5+1.523351100828001e+7).*(exp(-1.0e+1).*(3.0./1.0e+1)+(exp(-1.0e+1).*2.795151158657336e+5+1.523351100828001e+7).*(exp(-1.0e+1).*2.795148158657336e+5+T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+1.523349680828001e+7)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0,exp(-1.0e+1).*(3.0./1.0e+1)-(exp(-1.0e+1).*3.773617717226015e+5+2.056620155353675e+7).*(exp(-1.0e+1).*(3.0./1.0e+1)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)-(exp(-1.0e+1).*3.773617717226015e+5+2.056620155353675e+7).*(exp(-1.0e+1).*(3.0./1.0e+1)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)-(exp(-1.0e+1).*3.773617717226015e+5+2.056620155353675e+7).*(exp(-1.0e+1).*(3.0./1.0e+1)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)-(exp(-1.0e+1).*3.773617717226015e+5+2.056620155353675e+7).*(exp(-1.0e+1).*(3.0./1.0e+1)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)-(exp(-1.0e+1).*3.773617717226015e+5+2.056620155353675e+7).*(exp(-1.0e+1).*(3.0./1.0e+1)-(exp(-1.0e+1).*3.773617717226015e+5+2.056620155353675e+7).*(exp(-1.0e+1).*(3.0./1.0e+1)-(exp(-1.0e+1).*3.773617717226015e+5+2.056620155353675e+7).*(exp(-1.0e+1).*(3.0./1.0e+1)-(exp(-1.0e+1).*3.773617717226015e+5+2.056620155353675e+7).*(exp(-1.0e+1).*(3.0./1.0e+1)+(exp(-1.0e+1).*3.773617717226015e+5+2.056620155353675e+7).*(exp(-1.0e+1).*3.773614717226015e+5+T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+2.056618735353675e+7)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0)+7.1e+1./5.0)+7.1e+1./5.0)+7.1e+1./5.0)+7.1e+1./5.0)-T.*(exp(3.0).*(1.0e+1./3.0)-1.0e+1./3.0).*(3.0./5.0)+7.1e+1./5.0]
figure
semilogy(zzfcn(t))
zzm = reshape(zzfcn(t), [], numel(t));
Size_zzm = size(zzm)
Size_zzm = 1×2
11 11
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
[zz_min,zz_max] = bounds(zzm,'all')
zz_min = 5.1134e+50
zz_max = 1.3538e+73
figure
plot(t,yy,'+-')
hold on
plot(t, zzm,'o-'), grid
hold off
set(gca, 'YScale','log')
This gives a completely different result from the fplot plot.
..
