Differential equation in matlab Announcing the arrival of Valued Associate #679: Cesar...
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Differential equation in matlab
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 00:00UTC (8:00pm US/Eastern)Stochastic predator-preymatlab differential equationSolving 2nd order ODE with 2 independent parameters(over finite intervals), with bounds on solutionAnalytic solution to the one-compartment modelMatlab differential equation verificationIncluding a time delay term for a differential equationFinding parameters using two data sets for the same ODE systemmass balance from a system of nonlinear differential equationsDeciding the parameter value in a ODE systemHow can I solve/integerate the One-To-One kinetic binding model system of differential equations analytically?
$begingroup$
A pathogen population ($P(t)$) under the effect of a drug($A(t)$) is modelled as
${dPover dt}=rP-{E_{max}A^nover C_{50}^n+A^n}P$ and $A(t)$ is modelled as
$A(t)={Dover V}(e^{-k(t-t_0)}-e^{-k_a(t-t_0)})$.
From literature I know the values of $D,V,t_0$(lag time), $k,k_a$. So, $A(t)$ can be obtained at the respective time points the ODE is run.
$r,E_{max},n,C_{50}$ are also known.
I want to solve the ODE ${dPover dt}$ using ode45 of Matlab. (Without obtaining the analytical solution of $P(t)$ as this is only a simplified system and the original system cannot be solved analytically).
Can someone please let me know if the below code is right in solving $P(t)$. I am not sure about the way $A(t)$ is included into the ODE equation.
y0=10;
[t,y]=ode45(@Model,1:200,y0);
function s= Model(t,y)
r=0.4;
Emax=50;
n=1;
c_50=0.1;
k=0.25;
D=40;
V=6.6;
t0=1;
k_a=0.5;
s=zeros(1,1);
A=(D/V)*(exp(-k*(t-t0))-exp(-k_a*(t-t0)));
s(1)=r*y(1)-((Emax*(A^n))/((c_50^n)+(A^n)))*y(1);
end
ordinary-differential-equations matlab mathematical-modeling
asked Mar 25 at 10:17
sam_roxsam_rox
52321021
$endgroup$
add a comment |
$begingroup$
A pathogen population ($P(t)$) under the effect of a drug($A(t)$) is modelled as
${dPover dt}=rP-{E_{max}A^nover C_{50}^n+A^n}P$ and $A(t)$ is modelled as
$A(t)={Dover V}(e^{-k(t-t_0)}-e^{-k_a(t-t_0)})$.
From literature I know the values of $D,V,t_0$(lag time), $k,k_a$. So, $A(t)$ can be obtained at the respective time points the ODE is run.
$r,E_{max},n,C_{50}$ are also known.
I want to solve the ODE ${dPover dt}$ using ode45 of Matlab. (Without obtaining the analytical solution of $P(t)$ as this is only a simplified system and the original system cannot be solved analytically).
Can someone please let me know if the below code is right in solving $P(t)$. I am not sure about the way $A(t)$ is included into the ODE equation.
y0=10;
[t,y]=ode45(@Model,1:200,y0);
function s= Model(t,y)
r=0.4;
Emax=50;
n=1;
c_50=0.1;
k=0.25;
D=40;
V=6.6;
t0=1;
k_a=0.5;
s=zeros(1,1);
A=(D/V)*(exp(-k*(t-t0))-exp(-k_a*(t-t0)));
s(1)=r*y(1)-((Emax*(A^n))/((c_50^n)+(A^n)))*y(1);
end
ordinary-differential-equations matlab mathematical-modeling
asked Mar 25 at 10:17
sam_roxsam_rox
52321021
$endgroup$
$begingroup$
Matlab has a very comprehensive help with several examples. I urge you to check it.
$endgroup$
– Jon
Mar 25 at 11:06
add a comment |
$begingroup$
A pathogen population ($P(t)$) under the effect of a drug($A(t)$) is modelled as
${dPover dt}=rP-{E_{max}A^nover C_{50}^n+A^n}P$ and $A(t)$ is modelled as
$A(t)={Dover V}(e^{-k(t-t_0)}-e^{-k_a(t-t_0)})$.
From literature I know the values of $D,V,t_0$(lag time), $k,k_a$. So, $A(t)$ can be obtained at the respective time points the ODE is run.
$r,E_{max},n,C_{50}$ are also known.
I want to solve the ODE ${dPover dt}$ using ode45 of Matlab. (Without obtaining the analytical solution of $P(t)$ as this is only a simplified system and the original system cannot be solved analytically).
Can someone please let me know if the below code is right in solving $P(t)$. I am not sure about the way $A(t)$ is included into the ODE equation.
y0=10;
[t,y]=ode45(@Model,1:200,y0);
function s= Model(t,y)
r=0.4;
Emax=50;
n=1;
c_50=0.1;
k=0.25;
D=40;
V=6.6;
t0=1;
k_a=0.5;
s=zeros(1,1);
A=(D/V)*(exp(-k*(t-t0))-exp(-k_a*(t-t0)));
s(1)=r*y(1)-((Emax*(A^n))/((c_50^n)+(A^n)))*y(1);
end
ordinary-differential-equations matlab mathematical-modeling
asked Mar 25 at 10:17
sam_roxsam_rox
52321021
$endgroup$
A pathogen population ($P(t)$) under the effect of a drug($A(t)$) is modelled as
${dPover dt}=rP-{E_{max}A^nover C_{50}^n+A^n}P$ and $A(t)$ is modelled as
$A(t)={Dover V}(e^{-k(t-t_0)}-e^{-k_a(t-t_0)})$.
From literature I know the values of $D,V,t_0$(lag time), $k,k_a$. So, $A(t)$ can be obtained at the respective time points the ODE is run.
$r,E_{max},n,C_{50}$ are also known.
I want to solve the ODE ${dPover dt}$ using ode45 of Matlab. (Without obtaining the analytical solution of $P(t)$ as this is only a simplified system and the original system cannot be solved analytically).
Can someone please let me know if the below code is right in solving $P(t)$. I am not sure about the way $A(t)$ is included into the ODE equation.
y0=10;
[t,y]=ode45(@Model,1:200,y0);
function s= Model(t,y)
r=0.4;
Emax=50;
n=1;
c_50=0.1;
k=0.25;
D=40;
V=6.6;
t0=1;
k_a=0.5;
s=zeros(1,1);
A=(D/V)*(exp(-k*(t-t0))-exp(-k_a*(t-t0)));
s(1)=r*y(1)-((Emax*(A^n))/((c_50^n)+(A^n)))*y(1);
end
ordinary-differential-equations matlab mathematical-modeling
ordinary-differential-equations matlab mathematical-modeling
asked Mar 25 at 10:17
sam_roxsam_rox
52321021
asked Mar 25 at 10:17
sam_roxsam_rox
52321021
asked Mar 25 at 10:17
sam_roxsam_rox
52321021
asked Mar 25 at 10:17
sam_roxsam_rox
52321021
asked Mar 25 at 10:17
sam_roxsam_rox
52321021
52321021
$begingroup$
Matlab has a very comprehensive help with several examples. I urge you to check it.
$endgroup$
– Jon
Mar 25 at 11:06
add a comment |
$begingroup$
Matlab has a very comprehensive help with several examples. I urge you to check it.
$endgroup$
– Jon
Mar 25 at 11:06
$begingroup$
Matlab has a very comprehensive help with several examples. I urge you to check it.
$endgroup$
– Jon
Mar 25 at 11:06
$begingroup$
Matlab has a very comprehensive help with several examples. I urge you to check it.
$endgroup$
– Jon
Mar 25 at 11:06
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Your time vector likely has too large steps for solver. Try replace
1:200
with
linspace(0,0.125,256)
answered Mar 25 at 11:57
mathreadlermathreadler
15.6k72263
$endgroup$
$begingroup$
thank you for the answer.
$endgroup$
– sam_rox
Mar 25 at 13:07
add a comment |
$begingroup$
I copied your code to Octave (it runs most matlab code) and the results seem wrong, as the solution "explodes". This could be a precision in ode45. I attach the Wolfram Mathematica solution to the same problem. The solution decays to zero almost immediately.
answered Mar 25 at 11:12
PierreCarrePierreCarre
2,253215
$endgroup$
1
$begingroup$
It works just fine in Matlab if you just don't have too large delta t steps. 1:200 will give delta t of 1 everywhere which may be too large for many ODE solvers.
$endgroup$
– mathreadler
Mar 25 at 12:00
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Your time vector likely has too large steps for solver. Try replace
1:200
with
linspace(0,0.125,256)
answered Mar 25 at 11:57
mathreadlermathreadler
15.6k72263
$endgroup$
$begingroup$
thank you for the answer.
$endgroup$
– sam_rox
Mar 25 at 13:07
add a comment |
$begingroup$
Your time vector likely has too large steps for solver. Try replace
1:200
with
linspace(0,0.125,256)
answered Mar 25 at 11:57
mathreadlermathreadler
15.6k72263
$endgroup$
$begingroup$
thank you for the answer.
$endgroup$
– sam_rox
Mar 25 at 13:07
add a comment |
$begingroup$
Your time vector likely has too large steps for solver. Try replace
1:200
with
linspace(0,0.125,256)
answered Mar 25 at 11:57
mathreadlermathreadler
15.6k72263
$endgroup$
Your time vector likely has too large steps for solver. Try replace
1:200
with
linspace(0,0.125,256)
answered Mar 25 at 11:57
mathreadlermathreadler
15.6k72263
answered Mar 25 at 11:57
mathreadlermathreadler
15.6k72263
answered Mar 25 at 11:57
mathreadlermathreadler
15.6k72263
answered Mar 25 at 11:57
mathreadlermathreadler
15.6k72263
15.6k72263
$begingroup$
thank you for the answer.
$endgroup$
– sam_rox
Mar 25 at 13:07
add a comment |
$begingroup$
thank you for the answer.
$endgroup$
– sam_rox
Mar 25 at 13:07
$begingroup$
thank you for the answer.
$endgroup$
– sam_rox
Mar 25 at 13:07
$begingroup$
thank you for the answer.
$endgroup$
– sam_rox
Mar 25 at 13:07
add a comment |
$begingroup$
I copied your code to Octave (it runs most matlab code) and the results seem wrong, as the solution "explodes". This could be a precision in ode45. I attach the Wolfram Mathematica solution to the same problem. The solution decays to zero almost immediately.
answered Mar 25 at 11:12
PierreCarrePierreCarre
2,253215
$endgroup$
1
$begingroup$
It works just fine in Matlab if you just don't have too large delta t steps. 1:200 will give delta t of 1 everywhere which may be too large for many ODE solvers.
$endgroup$
– mathreadler
Mar 25 at 12:00
add a comment |
$begingroup$
I copied your code to Octave (it runs most matlab code) and the results seem wrong, as the solution "explodes". This could be a precision in ode45. I attach the Wolfram Mathematica solution to the same problem. The solution decays to zero almost immediately.
answered Mar 25 at 11:12
PierreCarrePierreCarre
2,253215
$endgroup$
1
$begingroup$
It works just fine in Matlab if you just don't have too large delta t steps. 1:200 will give delta t of 1 everywhere which may be too large for many ODE solvers.
$endgroup$
– mathreadler
Mar 25 at 12:00
add a comment |
$begingroup$
I copied your code to Octave (it runs most matlab code) and the results seem wrong, as the solution "explodes". This could be a precision in ode45. I attach the Wolfram Mathematica solution to the same problem. The solution decays to zero almost immediately.
answered Mar 25 at 11:12
PierreCarrePierreCarre
2,253215
$endgroup$
I copied your code to Octave (it runs most matlab code) and the results seem wrong, as the solution "explodes". This could be a precision in ode45. I attach the Wolfram Mathematica solution to the same problem. The solution decays to zero almost immediately.
answered Mar 25 at 11:12
PierreCarrePierreCarre
2,253215
answered Mar 25 at 11:12
PierreCarrePierreCarre
2,253215
answered Mar 25 at 11:12
PierreCarrePierreCarre
2,253215
answered Mar 25 at 11:12
PierreCarrePierreCarre
2,253215
2,253215
1
$begingroup$
It works just fine in Matlab if you just don't have too large delta t steps. 1:200 will give delta t of 1 everywhere which may be too large for many ODE solvers.
$endgroup$
– mathreadler
Mar 25 at 12:00
add a comment |
1
$begingroup$
It works just fine in Matlab if you just don't have too large delta t steps. 1:200 will give delta t of 1 everywhere which may be too large for many ODE solvers.
$endgroup$
– mathreadler
Mar 25 at 12:00
1
1
$begingroup$
It works just fine in Matlab if you just don't have too large delta t steps. 1:200 will give delta t of 1 everywhere which may be too large for many ODE solvers.
$endgroup$
– mathreadler
Mar 25 at 12:00
$begingroup$
It works just fine in Matlab if you just don't have too large delta t steps. 1:200 will give delta t of 1 everywhere which may be too large for many ODE solvers.
$endgroup$
– mathreadler
Mar 25 at 12:00
add a comment |
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$begingroup$
Matlab has a very comprehensive help with several examples. I urge you to check it.
$endgroup$
– Jon
Mar 25 at 11:06