Basic ODE question

So...it's been quite a while since I solved any systems of ODEs and I am admittedly very rusty. I am hoping there is a simple answer to this question:

I have a coupled system of ODEs:

dA/dc=-0.5*(2-v)*(1-v^2)/(1-v)

and

dv/dc=-1.5*(5-v)*(1-v^2)/(3-v)

Solve from c=[0 1]

Initial conditions: Ao=100, vo=0.5

How can I set this up in a Matlab function? Thanks for any advice!

Answer 1

[Matt Tearle]

1. Write a function that defines the rate equations. The system should now look like z' = f(c,z), where z = [A;v]. Write your function file so that it takes c and a vector z as inputs, and returns a vector dz that represents the derivatives ([A';v'])
2. Use ode45 to solve the system, giving a function handle to you function from step 2 as input, as well as the vector of start and end values for c and the initial conditions z0 = [A0;v0].
3. Extract the components of the solution returned by ode45 to plot as a function of c (also returned by ode45). (If A and v are on the same scale, you could just do plot(c,z))

Your question is mainly about step 1. So write a function file

function dz = functionname(c,z)
dz = zeros(size(z));
% extract components of z (ie A & c)
% define dz(1) according to the equation for dA/dc
% define dz(2) according to the equation for dv/dc

Answer 2

[Seth]

Solved the problem by simply decoupling and doing two independent ODE45 solves instead of treating as a system of equations. I understand this is not the best way - but worked fine for my problem.

Thanks Matt for the help.

Answer 3

[SHOBHIT KUMAR]

can we not just do this and find the solution from gtaph and get the answer?

sol=dsolve('Da=-0.5*(2-v)*(1-v^2)/(1-v)','a(0)=100','c');
ezplot(sol,[-2 2])
hold on;
s=dsolve('Dv=-1.5*(5-v)*(1-v^2)/(3-v)','v(0)=0.5','c');
ezplot(s,[-2 2])

Please answer

Answer 4

[jagathi medempudi]

What is the mat lab command for solving differential equation

Select one:

a. differentiation

b. dsolve

c. int

d. diff