Simultaneous equations with an integral

[mat.davies]

Hello

I am having a problem solving a set of simultaneous equations in mathematica. One of the equations is an integral, with the unkowns as limits of integration, and the other is a function containing both variables, but no closed form solution can be found for either variable. I am therefore attempting to solve it numerically.

I have tried both FindRoot and NSolve, and i get the same error for both, namely that algebraic limits cannot be supplied with Nintegrate. Below is a sample of what I'm trying to do (I have replaced the functions with simpler examples to avoid confusion - I am aware that this problem does not need to be solved numerically!)

f[s_] := 2 s
NSolve[{NIntegrate[f[s], {s, (a + b)/2, a + 2 b}] == 0, a - 2 b + 2 == 0. {a, b}]

Apologies if i the above code has errors, I have had to copy it from one machine to another, and may have made a mistake in doing so.

Any help would be greatly appreciated.

Mat Davies

 

[mat.davies]

I have now solved this problem

For the record, the messages were only warnings in the above code, but they were errors in my original code. The solution was to use the more stable FindMinimum function

Thanks

mat

 

[oswaler]

Dear Mat Davies,

Thank you for reaching out to us with your problem. Simultaneous equations with an integral can be tricky to solve, especially when there is no closed form solution. I can understand your frustration with the error message you are receiving.

One possible solution to this problem is to use the numerical integration function NIntegrate within the NSolve command. This will allow you to solve the equations simultaneously and find a numerical solution for the limits of integration. For example:

f[s_] := 2 s
NSolve[{NIntegrate[f, {s, (a + b)/2, a + 2 b}] == 0, a - 2 b + 2 == 0. {a, b}, Method -> "NIntegrate"]

Using the "NIntegrate" method within NSolve will instruct Mathematica to use numerical integration to solve the equations. This should resolve the error you were receiving.

I hope this helps and please let me know if you have any further questions or concerns. Good luck with your research!

Best regards,