Need help having a problem with shooting mthd

[arditi]

need help please having a problem with shooting mthd

i am having a problem coding a MATLAB code for the given eqn

d^2T/dx^2 - 1*10^-7(T+273)^4+4(150-T)=0
BC T(0)=200 and T(0.5)=100

the differential equation should be solved by
the function ODE23, and the consistent initial condition should be found by the
function FZERO in Matlab. I have to reduce the problem to a root finding
problem somehow, but i just can't do it.
please help me

 

[MATLABdude]

Welcome to PhysicsForums!

I myself am hazy on the Shooting Method, but you may want to start here (or in your notes / textbook):
http://en.wikipedia.org/wiki/Shooting_method

...And for future reference, homework questions like this more properly belong in the Engineering and Computing Science homework forum.

 

[oswaler]

Hello,

Thank you for reaching out for help with your coding problem. I understand that you are trying to solve a differential equation using MATLAB and are having trouble with the shooting method. It sounds like you are on the right track by using the ODE23 and FZERO functions, but are struggling with reducing the problem to a root finding problem.

One possible approach could be to use the bisection method to find the root of the equation. This method involves dividing the interval between the two boundary conditions (T(0) and T(0.5)) into smaller intervals and checking for a sign change in the function. Once a sign change is found, the root can be approximated by taking the midpoint of the interval. This process can be repeated until the desired level of accuracy is achieved.

Another option could be to use the shooting method in combination with a solver like fsolve to find the root of the equation. This involves guessing an initial condition for T(0.5) and solving the differential equation using ODE23. If the resulting value of T(0.5) does not match the desired boundary condition, the guess can be adjusted and the process can be repeated until the desired accuracy is achieved.

I recommend consulting with a colleague or mentor for further assistance and guidance on implementing these methods in your code. Best of luck with your project!