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In[]:=
ClearAll["Global`*"];
In[]:=
α[i_]:=1
In[]:=
g0=0.9;b10=0.03;b11=0.001;Topt=24;gama0=150;ds0=4;A0=0.2;w=2.10;z1=3.5;Oc=1.10;d1=0.66;d=0.4;gama1=2;d2=0.2;z=0.0019;β=1.024;γ=4;z0=10.10;T10=14.50;delta1=0.1;T0=20;b=1.30;Tmaks=35;
In[]:=
K=1;M=1201.;T=60.05;
In[]:=
x[t_]
0,0
:=10;
h1[t_]
0,0
:=28;
h2[t_]
0,0
:=1;
y[t_]
0,0
:=1.2;
z[t_]
0,0
:=0.25;
In[]:=
x[λ_]
m_
:=ParallelSum
x[t]
m,i
*
i
λ
,{i,0,K};
h1[λ_]
m_
:=ParallelSum
h1[t]
m,i
*
i
λ
,{i,0,K};
h2[λ_]
m_
:=ParallelSum
h2[t]
m,i
*
i
λ
,{i,0,K};
y[λ_]
m_
:=ParallelSum
y[t]
m,i
*
i
λ
,{i,0,K};
z[λ_]
m_
:=ParallelSum
z[t]
m,i
*
i
λ
,{i,0,K};
In[]:=
N
1
[λ_]
m_
:=g0*Exp-b*
h1[λ]
m
-Topt
Tmaks-Topt
+
z[λ]
m
-b10+b11*
h1[λ]
m
-Topt
z[λ]
m
+1
*
x[λ]
m
-
g0*
x[λ]
m
^2
gama0
;
N
2
[λ_]
m_
:=w*
h2[λ]
m
-z1*
h1[λ]
m
-T10+γ*z0-
y[λ]
m
;
N
3
[λ_]
m_
:=A0-delta1*
h2[λ]
m
;
N
4
[λ_]
m_
:=Oc-d1*
y[λ]
m
-d*
y[λ]
m
*
h2[λ]
m
;
N
5
[λ_]
m_
:=gama1*
h1[λ]
m
-T0
β
*
ds0
1+
h1[λ]
m
-Topt
-
z[λ]
m
-d2*
z[λ]
m
*
x[λ]
m
-z*
h1[λ]
m
-Topt;
In[]:=
A
1
m_,0
:=
N
1
[0]
m
;
A
2
m_,0
:=
N
2
[0]
m
;
A
3
m_,0
:=
N
3
[0]
m
;
A
4
m_,0
:=
N
4
[0]
m
;
A
5
m_,0
:=
N
5
[0]
m
;
In[]:=
TimingDoFori=0,i<K,i++,
A
1
m,i
=Simplify
1
i!
*D
N
1
[λ]
m
,{λ,i}/.λ0;
A
2
m,i
=
1
i!
*D
N
2
[λ]
m
,{λ,i}/.λ0;
A
3
m,i
=
1
i!
*D
N
3
[λ]
m
,{λ,i}/.λ0;
A
4
m,i
=
1
i!
*D
N
4
[λ]
m
,{λ,i}/.λ0;
A
5
m,i
=
1
i!
*D
N
5
[λ]
m
,{λ,i}/.λ0;Do
x[t_]
m,k
=
1
Gamma[α[1]]
*Integrate
α1-1
(t-τ)
*
A
1
m,k-1
,{τ,0,t};
h1[t_]
m,k
=
1
Gamma[α[1]]
*Integrate
α2-1
(t-τ)
*
A
2
m,k-1
,{τ,0,t};
h2[t_]
m,k
=
1
Gamma[α[1]]
*Integrate
α3-1
(t-τ)
*
A
3
m,k-1
,{τ,0,t};
y[t_]
m,k
=
1
Gamma[α[1]]
*Integrate
α4-1
(t-τ)
*
A
4
m,k-1
,{τ,0,t};
z[t_]
m,k
=
1
Gamma[α[1]]
*Integrate
α5-1
(t-τ)
*
A
5
m,k-1
,{τ,0,t},{k,1,K};
f1[t_]
m_
:=ParallelSum
x[t-(T/M)*m]
m,i
,{i,0,K};
f2[t_]
m_
:=ParallelSum
h1[t-(T/M)*m]
m,i
,{i,0,K};
f3[t_]
m_
:=ParallelSum
h2[t-(T/M)*m]
m,i
,{i,0,K};
f4[t_]
m_
:=ParallelSum
y[t-(T/M)*m]
m,i
,{i,0,K};
f5[t_]
m_
:=ParallelSum
z[t-(T/M)*m]
m,i
,{i,0,K};
x[t_]
m+1,0
=
f1[(T/M)*(m+1)]
m
;
h1[t_]
m+1,0
=
f2[(T/M)*(m+1)]
m
;
h2[t_]
m+1,0
=
f3[(T/M)*(m+1)]
m
;
y[t_]
m+1,0
=
f4[(T/M)*(m+1)]
m
;
z[t_]
m+1,0
=
f5[(T/M)*(m+1)]
m
,{m,0,M-1};
X[t_]:=X[t]=PiecewiseParallelTable
f1[t]
m
,((T/M)*(m))<=t<((T/M)*(m+1)),{m,0,M-1};
H1[t_]:=H1[t]=PiecewiseParallelTable
f2[t]
m
,((T/M)*(m))<=t<((T/M)*(m+1)),{m,0,M-1};
H2[t_]:=H2[t]=PiecewiseParallelTable
f3[t]
m
,((T/M)*(m))<=t<((T/M)*(m+1)),{m,0,M-1};
Y[t_]:=Y[t]=PiecewiseParallelTable
f4[t]
m
,((T/M)*(m))<=t<((T/M)*(m+1)),{m,0,M-1};
Z[t_]:=Z[t]=PiecewiseParallelTable
f5[t]
m
,((T/M)*(m))<=t<((T/M)*(m+1)),{m,0,M-1};
s1=ParallelTable[{t,X[t]},{t,0,T}];
In[]:=
s1MSADM=ListLinePlot[s1,PlotRangeAll,PlotStyleBlack,AxesLabel{"t","N(t)"}]
Out[]=
s2=ParallelTable[{t,H1[t]},{t,0,T}];
In[]:=
s2MSADM=ListLinePlot[s2,PlotRangeAll,PlotStyleBlack,AxesLabel{"t","T(t)"}]
Out[]=
s3=ParallelTable[{t,H2[t]},{t,0,T}];
In[]:=
s3MSADM=ListLinePlot[s3,PlotRangeAll,PlotStyleBlack,AxesLabel{"t","C(t)"}]
Out[]=
s4=ParallelTable[{t,Y[t]},{t,0,T}];
In[]:=
s4MSADM=ListLinePlot[s4,PlotRangeAll,PlotStyleBlack,AxesLabel{"t","Z(t)"}]
Out[]=
s5=ParallelTable[{t,Z[t]},{t,0,T}];
In[]:=
s5MSADM=ListLinePlot[s5,PlotRangeAll,PlotStyleBlack,AxesLabel{"t","U(t)"}]
Out[]=
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