ode45 Initial conditions are not at the same point

Hello everybody, I'm using ode45 to solve some easy differential equations.

Here are the equations that I have:

For now, I have the initial conditions:

As you can see, the initial conditions are in not the common case, which may look like:x(4)=a;y(4)=b;

The value of x and y gets from different point.

Any suggestion on the set of initial values for ode45?

Thank you in advance!

Meredith

Answer 1

[madhan ravi]

https://www.mathworks.com/help/matlab/ref/bvp4c.html

[Yijia Liu]

bvp4c seems to solve the multi-boundary problem of the same variable, that the initial conditions all get from y. If the two given initial conditions one is from x, another is from y, can I use bvp4c to sovle it?

Thanks for your answer!

[Torsten]

The ODE solvers work with one arrays for the solution variables (e.g. z), not with multiple single expressions (x,y). So for both ODE45 and BVP4C you will have to rename your variables as

x=z(1), y=z(2)

e.g.

And BVP4C is the adequate tool to solve your exercise.

[madhan ravi]

Thank you Torsten :)

[Yijia Liu]

Thanks for your help!

[madhan ravi]

Anytime :) if you find the answer helpful and it answered your query make sure to accept the answer

Answer 2

[Pasindu Ranasinghe]

Example Code

Use ode45() to find the approximate values of the solution at t in the range of 1 to 3

function ydot = eqns(t,y)
ydot=(t-exp(-t))/(y+exp(y));
end

###################################
%%Code
[t1,y1]=ode45(@eqns,[1.5 1], 0.5);
hold on;
[t2,y2]=ode45(@eqns,[1.5 3], 0.5);
hold off
t=[t1;t2];
y=[y1;y2];
plot(t,y,'-o')

HOPE YOU FIND THIS USEFULL