Solving a third order non-linear ode using ode45
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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 个评论
Shiv Patel
2017-11-17
Thank you for this comment, it helped with my homework!
回答（4 个）
Star Strider
2012-10-28
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 个评论
Star Strider
2012-11-1
I'm glad I could help.
In the bvp4c version, changing the bvpinit call to:
SolYinit = bvpinit([0 5], [0; 0; 0]);
produces substantially the same curves as your code, with slightly greater magnitudes by a factor of about 1.4 between 0 and 3. Setting the third initial condition to 1.3 doesn't appear to make a significant difference. I didn't see a difference in your and my differential equation functions, other than I set mine up as an anonymous function.
Ngoc-Tram Le
2015-11-7
Thanks a lot for your sharing this code. I got the same problem like that.
Saeid
2020-7-6
I have to solve a very similar problem:
F''' + 1 - F'^2 = 0
But my BCs are different:
F'(0)=F"(inf)=0
F'(inf)=1
I formulate the problem exactly as suggested above:
dYdX = @(X,Y) [Y(2); Y(3); Y(2).^2-1]; % Differential equation
res = @(ya,yb) [ya(2); yb(3); yb(2)-1];
But when I try Star Strider's method it generates the Jacobian error. Could it be that the BCs do not contain F(...)?
David After
2020-9-4
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
2020-9-4
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
R Vishnu
2014-1-30
0 个投票
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.
Hemanth kumar C
2017-11-8
0 个投票
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 个评论
Torsten
2017-11-17
I don't understand your equations.
If fi, Phi and thetha are your dependent variables and y is the independent variables, what does dc/dy, dt/dy mean in your equations ?
Please clarify which variables are given constants, dependent and independent variables.
The best will be to delete your question (answer ?) here and open a new thread.
Best wishes
Torsten.
Hemanth kumar C
2017-12-7
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
2017-12-7
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.
David After
2020-9-4
0 个投票
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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