Dtjytyk

Why do early math courses focus on the cross sections of a cone and not on other 3D objects?

Why wasn't DOSKEY integrated with COMMAND.COM?

Is it possible for SQL statements to execute concurrently within a single session in SQL Server?

Can a new player join a group only when a new campaign starts?

How could we fake a moon landing now?

How often does castling occur in grandmaster games?

Morning, Afternoon, Night Kanji

Selecting user stories during sprint planning

How can I reduce the gap between left and right of cdot with a macro?

How would a mousetrap for use in space work?

Can the Great Weapon Master feat's damage bonus and accuracy penalty apply to attacks from the Spiritual Weapon spell?

Putting class ranking in CV, but against dept guidelines

How do I use the new nonlinear finite element in Mathematica 12 for this equation?

What order were files/directories outputted in dir?

Project Euler #1 in C++

Is there hard evidence that the grant peer review system performs significantly better than random?

How to react to hostile behavior from a senior developer?

Amount of permutations on an NxNxN Rubik's Cube

Generate an RGB colour grid

Effects on objects due to a brief relocation of massive amounts of mass

How does the math work when buying airline miles?

Do wooden building fires get hotter than 600°C?

Why is it faster to reheat something than it is to cook it?

Sum letters are not two different

Differential equation in matlab

1

$begingroup$

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

share|cite|improve this question

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 | 

1

$begingroup$

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

share|cite|improve this question

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

share|cite|improve this question

asked Mar 25 at 10:17

sam_roxsam_rox

52321021

$endgroup$

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

share|cite|improve this question

asked Mar 25 at 10:17

sam_roxsam_rox

52321021

share|cite|improve this question

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

2 Answers
2

active

oldest

votes

1

$begingroup$

Your time vector likely has too large steps for solver. Try replace

1:200

with

linspace(0,0.125,256)

share|cite|improve this answer

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 | 

0

$begingroup$

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.

share|cite|improve this answer

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 | 

Your Answer

StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});

function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});


}
});

draft saved

draft discarded

Sign up or log in

StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name

Email

Required, but never shown

StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3161601%2fdifferential-equation-in-matlab%23new-answer', 'question_page');
}
);

Post as a guest

Name

Email

Required, but never shown

1

$begingroup$

Your time vector likely has too large steps for solver. Try replace

1:200

with

linspace(0,0.125,256)

share|cite|improve this answer

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 | 

1

$begingroup$

Your time vector likely has too large steps for solver. Try replace

1:200

with

linspace(0,0.125,256)

share|cite|improve this answer

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)

share|cite|improve this answer

answered Mar 25 at 11:57

mathreadlermathreadler

15.6k72263

$endgroup$

1:200

linspace(0,0.125,256)

share|cite|improve this answer

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

0

$begingroup$

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.

share|cite|improve this answer

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 | 

0

$begingroup$

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.

share|cite|improve this answer

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.

share|cite|improve this answer

answered Mar 25 at 11:12

PierreCarrePierreCarre

2,253215

$endgroup$

share|cite|improve this answer

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