Solving a system of ODE with BCs

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Elia Paini
Elia Paini 2021-4-20
评论： Elia Paini 2021-4-24
Hi, I'm trying to solve a system of 2 ODE with boundary conditions.
The integration variable is r, which is the sferical coordinate (radius of a sphere). At the end of the simulation I should get the values of A and B as a functions of r, where the maximum value of r is 1.
k,c,a,b are constants.
The system is as follows:
Equations:
BCs:
I converted the system to first order one, as follows:
Equations:
BCs:
Y3(0)=Y4(0)=0
Y1(1)=a
Y2(1)=b
How can I solve it?
Thank you!

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Divija Aleti
Divija Aleti 2021-4-23
Hi Elia,
The following link gives an example of how to solve a system of two first-order differential equations with boundary conditions. Similarly, you can solve for your converted system of four first order differential equations.
Solve a System of Differential Equations
Hope this helps!
Regards,
Divija
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Elia Paini
Elia Paini 2021-4-24
I tried to use the way you suggested me, but Matlab can't find a solution. The message is as follows:
Warning: Unable to find symbolic solution.
I think that, because the complexity of the system, bvp4c must be used. In this way, results are correct.

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