ODE45 for a second order differential equation

I have a second order differential equation : y''=(2*y)+(8*x)*(9-x); Boundary Conditions y(0)=0 , y(9)=0 Need to solve the diff eq using ode45.

I've tried watching a bunch of tutorials but I just cannot seem to figure out how the function is written as a column vector [y';y'']. I don't understand it at all and that might make this query vague too.

Hope someone can help with the code or the explanation on how to solve the above.

Thank you

Answer 1

[Torsten]

[x,y] = ode45(@fun,[0 9],[0 -28]);

function dy = fun(x,y)
dy = zeros(2,1);
dy(1) = y(2);
dy(2) = 2*y(1)+8*x*(9-x);

But for a boundary value problem like yours, you will have to use "bvp4c" instead of "ode45".

Best wishes

Torsten.

[Remston Martis]

Error :

>> [x,y] = ode45(@fun,[0 9],[0 -28]);
Attempt to execute SCRIPT ode45 as a function:
C:\Users\remst\Desktop\ode45.m

using bvp4c says too many input arguments.

[Torsten]

Put

function main
[x,y] = ode45(@fun,[0 9],[0 -28]);

function dy = fun(x,y)
dy = zeros(2,1);
dy(1) = y(2);
dy(2) = 2*y(1)+8*x*(9-x);

in one file, name it main.m and execute it as a function file.

Best wishes

Torsten.

[Remston Martis]

Just doesn't seem to work .

Error Message: Attempt to execute SCRIPT ode45 as a function: C:\Users\remst\Desktop\ode45.m

Error in main (line 2) [x,y] = ode45(@fun,[0 9],[0 -28]);

I tried running the script and I tried calling the function in the commany window. Gives me the same error.

[Torsten]

There seems to be a duplicate of ode45 on your desktop - rename or remove it.

[Remston Martis]

Brilliant. Thank you Torsten!

Answer 2

[Stephan]

Hi,

transform a n-th order ode into a system of n 1st order ode's to solve it.

Matlab documentation example: https://de.mathworks.com/help/matlab/math/solve-nonstiff-odes.html

More examples here: https://www.google.de/url?sa=t&source=web&rct=j&url=http://www.math.poly.edu/courses/ma2132/Notes/MA2132EquationsToSystems.pdf&ved=2ahUKEwiQ_tCRq83aAhWMMewKHQ7CC1IQFjALegQIBxAB&usg=AOvVaw07Im9F42d9LrfvRIzL35Pd

If you read this i guess you can quickly solve your problem.

[Remston Martis]

I keep getting these errors: Attempt to execute SCRIPT ode45 as a

function: C:\Users\remst\Desktop\ode45.m

Error in ode45 (line 3) [x,y] = ode45(@fun,[0 9],[0 -28]);

My function declarations are:

function fun=fun(x,y)
fun=zeroes(2,1);
fun(1)=y(2);
fun(2)=(2*y(1))+8*x*(9-x);

Calling the function :

[x,y] = ode45(@fun,[0 9],[0 -28]);

Where am I going wrong? I've tried 10000s of ways

[Ebraheem Menda]

In this case you have declared the name of the function and its output both with the same name 'fun'. That is the problem it seems.

Answer 3

[NARSIRAM GURJAR]

C:\Users\remst\Desktop\ode45.m

save this file with different name