DIfferential equation (ODE)

Hy everyone!

I would like to make mathematical modelling in MATLAB, but I can't get my head around it. So here it is the equation:

dc/dt = -r

-r = (kreac*Kads*(c))/(1+Kads*(c))

c(0)=125 micromol

Kads = 4.45*10^-2

kreac = 2.06*10^-2

t(0) = 0

t(f) = 120

How can I solve this in MATLAB?

[John D'Errico]

What have you tried? Have you tried dsolve? ode45? If nothing, then why not make an effort? This is a basic ODE problem. Take a shot at it. Read the help for those tools. Look at the examples. Show what you tried, and ask what you did wrong. You will get more help if you show a willingness to make an effort than if you just post a doit4me.

[István Székely]

You are right. I have tried dsolve and ode45 also, but I was not able to run the script. I have used Polymath also, there I had success, but limited success.

Answer 1

[Ennio Condoleo]

Hey, I would like to propose you a hint. This is a classical problem to be solved by using ODE. Let's assume the following differential equation at first order:

dc/dt = (k1*k2*c)/(1+k2*c)

where k1 and k2 are real values. The initial condition c = c0 is assigned at t = t0. The final time of integration is t = tf.

A fast solution to this issue is:

odeOptions = odeset('RelTol',1e-6,'AbsTol',1e-8);
t0 = 0;
tf = 120;
c0 = 125;
k1 = 2.06e-2;
k2 = 4.45e-2;
[t,c] = ode45(@myfun,[t0,tf],c0,odeOptions,k1,k2);
plot(t,c);

where "myfun" is a function as:

function [c] = myfun(t,c,k1,k2)
c = (k1*k2*c)/(1+k2*c);

[István Székely]

Thank you!