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 Kommentar
Antworten (4)
Star Strider
am 28 Okt. 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 Kommentare
David After
am 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
am 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
R Vishnu
am 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.
Hemanth kumar C
am 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 Kommentare
Hemanth kumar C
am 7 Dez. 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
am 7 Dez. 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.
David After
am 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
0 Kommentare
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