solve a system of ode by bvp4c
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Hi, I am trying so solve a system of boundary value problem. I have tried looking into the examples given yet I still have problem in writing the code and running the program.
Briefly, I have 3 equations to solve. I have convert them to first order system in order to put it in matlab. Where, I let W=y1, W'=y2, U=y3, U'=y4, U''=y5, V=y6, V'=y7, V''=y8. I have the boundary 0f x from [0 infinity], and I choose infinity=20. I also need to plot graphs of x-axis:x (from 0 to 20) for y-axis:U, V and W respectively.
I know there are lots of mistakes here hence please correct me if Im wrong. I have attached the code here.
Thank you :))
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Taylor Nichols
2019년 1월 24일
how did you arange the boundary conditions in your code if you don't mind me asking?
I've only done a ODE with one dependent variable in which I arranged my conditions this way
This is a 4th order equation btw.
bc = [yl(1) - hi;
yl(2);
yr(1) - ho;
yr(2)];
채택된 답변
Torsten
2016년 1월 15일
Solve your equations for W', U'' and V''.
Let
y(1) = W, y(2) = U, Y(3) = U', Y(4) = V, Y(5) = V'.
Your system then reads
Y(1)' = F0(Y(1),Y(2),Y(3),Y(4),Y(5))
Y(2)' = Y(3)
Y(3)' = F1(Y(1),Y(2),Y(3),Y(4),Y(5))
Y(4)' = Y(5)
Y(5)' = F2(Y(1),Y(2),Y(3),Y(4),Y(5))
Now use one of the ODE solvers in the usual manner.
Best wishes
Torsten.
댓글 수: 3
Torsten
2016년 1월 15일
편집: Torsten
2016년 1월 15일
Order equations (2) and (3) such that they look like
a1*U'' + b1*V'' = c1
a2*U'' + b2*V'' = c2
with a1, b1, c1, a2, b2, c2 expressions only depending on U, U', V, V', W and W'.
Then solve this (linear) system of equations from above for U'' and V'':
U'' = (c1*a2-c2*a1)/(b1*a2-b2*a1)
V'' = -(c1*b2-c2*b1)/(b1*a2-b2*a1)
Best wishes
Torsten.
P.S.: It seems you forget parentheses around expressions, e.g. (1-n/n+1) should be (1-n/(n+1)), I guess.
추가 답변 (1개)
Torsten
2016년 1월 18일
I mean that the function F1 from above is given by
F1(W,U,U',V,V') = (c1*a2-c2*a1)/(b1*a2-b2*a1)
and the function F2 from above by
F2(W,U,U',V,V') = -(c1*b2-c2*b1)/(b1*a2-b2*a1)
Now you can define your array "dydx" in function "ex11ode" by
dydx = [-2Y(2)+x(1-n/n+1)Y(3)
Y(3)
F1(Y(1),Y(2),Y(3),Y(4),Y(5))
Y(5)
F2(Y(1),Y(2),Y(3),Y(4),Y(5))]
Best wishes
Torsten.
댓글 수: 9
Torsten
2016년 1월 25일
Something like
c=(sol.y(4,:).^2+sol.y(5,:).^2).^((1-n)/(n+1));
plot(sol.x,c);
after the call to bvp4c should work.
Best wishes
Torsten.
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