Let us assume k intervals (, ), (, + ), ..., (, + ), with k constant and positive continuous intakes , i = 1, 2, k respectively The observed quantity y(t) retained in the body at time t can be modeled as:
s
i
T
1
s
2
s
2
T
2
s
k
s
k
T
k
b
i
R(t)=(t)+(t)....+(t)+ϵ(t)=(t),t∈[1,+]
b
1
q
1
b
2
q
2
b
k
q
k
k
∑
i=1
b
i
q
i
s
k
T
k
where
In[]:=
qMultiple1[inputdata_,{ff_,tt_},ts_]:=Module[{u,uc,tau,r,rr,rt,bi,t1,ti,Ti,t2,t3},u[t2_]=ff/.tt->t2;uc[t3_]=Integrate[u[tau],{tau,0,t3}];r[t1_,Ti_]:=Piecewise[{{0,t1<0},{uc[t1],0<=t1<=Ti},{uc[t1]-uc[t1-Ti],t1>Ti}}];rr[bi_,ti_,Ti_]:=(bi/Ti)*r[t1-ti,Ti];rt=rr@@@inputdata/.t1->ts;Total[rt]];
In[]:=
qMultiple2[inputdata_,{ff_,tt_},ts_]:=Module[{tau,r,rr,rt,bi,t1,ti,Ti,t2,t3},u[t2_]=ff/.tt->t2;r[t1_,Ti_]:=Piecewise[{{0,t1<0},{uc[t1],0<=t1<=Ti},{uc[t1]-uc[t1-Ti],t1>Ti}}];rr[bi_,ti_,Ti_]:=(bi/Ti)*r[t1-ti,Ti];rt=rr@@@inputdata/.t1->ts;Total[rt]];
In[]:=
u[t_]=1/2-1/2;
-0.5t
-2t
In[]:=
inputs={{100,0,10},{30,15,10},{15,30,5}};
In[]:=
uc[t3_]=Integrate[u[tau],{tau,0,t3}];
In[]:=
Plot[qMultiple1[inputs,{u[t],t},t1],{t1,0,50},ExclusionsStyle{Blue,Blue}]//AbsoluteTiming
Out[]=
21.061,
In[]:=
Plot[qMultiple2[inputs,{uc[t],t},t1],{t1,0,50},ExclusionsStyle{Blue,Blue}]//AbsoluteTiming
Out[]=
0.219023,