Solving a third order non-linear ode using ode45

10 vues (au cours des 30 derniers jours)
Abhinav
Abhinav le 28 Oct 2012
Commenté : David After le 4 Sep 2020
I need to solve
F''' + 2FF" + 1 - F'^2 = 0
with the boundary conditions
F(0)=F'(0)=0 and F'(infinity)=1.
I am new to using the ode solver in matlab and am not sure how to make it solve a non-linear third order equation. Any suggestion would be appreciated.
  1 commentaire
Shiv Patel
Shiv Patel le 17 Nov 2017
Thank you for this comment, it helped with my homework!

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Réponses (4)

Star Strider
Star Strider le 28 Oct 2012
The ode45 function is not applicable to two-point boundary value problems such as yours. You need to use bvp4c for example, as I did here:
dYdX = @(X,Y) [Y(2); Y(3); Y(2).^2-Y(1).*Y(2).*2.0-1.0]; % Differential equation
res = @(ya,yb) [ya(1); ya(2); yb(2)-1]; % Boundary conditions
SolYinit = bvpinit([0 1E+1], [1; 1; 1]);
Fsol = bvp4c(dYdX, res, SolYinit);
X = Fsol.x;
F = Fsol.y;
figure(1)
plot(X, F)
legend('F_1', 'F_2', 'F_3', 3)
grid
You will not be able to set your endpoint to Inf or other number larger than about 10 (at least I could not) because that generates a singular Jacobian (or so MATLAB tells me). There are links to bvpinit and the other functions throughout and at the end of the bvp4c page. You might also want to experiment with bvp5c.
This was an interesting problem. I am glad you asked the question.
  6 commentaires
David After
David After le 4 Sep 2020
How can i solve this eqaution?
F''' (eta)+ F(eta)F"(eta) + F'^2(eta) = 0
with the boundary conditions
F(0)=F''(0)=0 and F'(infinity)=0 and eta is 0:0.1:6
i want to plot it and create a table for it (eta-f-f'-f'')
I am new to using the ode solver in matlab and am not sure how to make it solve a equation. Any suggestion would be appreciated.
thank you
my email : ff223325@gmail.com
David After
David After le 4 Sep 2020
How can i solve this eqaution?
F''' (eta)+ F(eta)F"(eta) + F'^2(eta) = 0
with the boundary conditions
F(0)=F''(0)=0 and F'(infinity)=0 and eta is 0:0.1:6
i want to plot it and create a table for it (eta-f-f'-f'')
I am new to using the ode solver in matlab and am not sure how to make it solve a equation. Any suggestion would be appreciated.
thank you
my email : ff223325@gmail.com

Connectez-vous pour commenter.


R Vishnu
R Vishnu le 30 Jan 2014
Hi I hope to correct a minor error. it is f(3) = -1 -2*y(1)*y(2) + y(2)*y(2); and not f(3) = -1 -2*y(1)*y(3) + y(2)*y(2); as per your equation F''' + 2FF' + 1 - (F'^2) = 0.
  1 commentaire
Abhinav
Abhinav le 30 Jan 2014
Hi Vishnu, My bad.. the second term was supposed to be 2FF". I have edited the original question too.
Thanks for pointing that out!

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Hemanth kumar C
Hemanth kumar C le 8 Nov 2017
I need to solve
(D^2-a^2)fi+a*[R*thetha+(Ra*Phi/Le)] = 0,
(D^2-a^2)thetha-(a*(dt/dy)*fi)-Pe*D(thetha)+gamma*Phi=0,
(D^2-a^2)Phi-Le*Pe*D(Phi)-a*le*(dc/dy)*fi=0
with the boundary conditions y=0;fi=Phi=thetha=0
I am new to using the ode solver in matlab and am not sure how to make it solve a non-linear second order three equation and i have written the program but i am not getting proper output . if you want to see my practise paper i will attach here . Any suggestion would be appreciated.
  3 commentaires
Hemanth kumar C
Hemanth kumar C le 7 Déc 2017
dc/dy ,dt/dy are the temperature and concentration gradients.i derived equations for that. i attached the program sir you can see the both equations
Hemanth kumar C
Hemanth kumar C le 7 Déc 2017
i am solving this above attached paper .i derived everything only programming part i am not getting few things .please help me to solve this problem. you can see what is dc/dy and dt/dy in the paper.

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David After
David After le 4 Sep 2020
How can i solve this eqaution?
F''' (eta)+ F(eta)F"(eta) + F'^2(eta) = 0
with the boundary conditions
F(0)=F''(0)=0 and F'(infinity)=0 and eta is 0:0.1:6
i want to plot it and create a table for it (eta-f-f'-f'')
I am new to using the ode solver in matlab and am not sure how to make it solve a equation. Any suggestion would be appreciated.
thank you
my email : ff223325@gmail.com

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