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

### Prabhakar (view profile)

on 18 Jan 2011
Latest activity Commented on by Taswald Moodley

### Taswald Moodley (view profile)

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?

### Yuki (view profile)

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

Taswald Moodley

### Taswald Moodley (view profile)

on 19 Nov 2019 at 21:21
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.