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How to solve a system of ODEs involving integral constraints using BVP4C in MATLAB 7.11 (R2010b)?

Asked by Prabhakar on 18 Jan 2011
Latest activity Commented on by Taswald Moodley on 19 Nov 2019 at 21:21
I am trying to solve a system of ODEs with associated boundary conditions and integral constraints. How to incorporatethe integral constraints into BVP4C?

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Answer by Yuki
on 18 Jan 2011

There is no direct mechanism to incorporate integral constraints using BVP4C. A work around is to convert the integral constraints into differential constraints by introducing additional states. For example, consider the following problem:
Solve: x_1’ = x_2x_2’ = 1 Subject to the boundary constraints : x_1(0)=0 [integral(x_2^2) from 0 to 1] = 5.
To solve this problem, introduce an additional state x_3 such that, x_3’ = x_2^2 with boundary conditions: x_3(0)=0 x_3(1)=5.
Now you can use BVP4C to solve the following system of 3 ODEs with 3 boundary conditions: x_1’ = x_2 x_2’ = 1 x_3’=x_2^2 x_1(0)=0 x_3(0)=0 x_3(1)=5

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Please can you post the actual code needed to perform your example given. I am struggling with a similiar example involving an integral boundary condition and would appreciate it seeing the code.

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