I have a project where I need to solve

T''(x) = bT^4 ; 0<=x<=1

T(0) = 1

T'(1) = 0

using finite differences to generate a system of equations in Matlab and solve the system to find the solution

So far I have:

(using centred 2nd degree finite difference)

T''(x) = (T(x+h) - 2T(x) + T(x-h)) / h^2 = bT(x)^4

and

(using 2 order backward difference)

T'(x) = (3T(x) - 4T(x-h) + T(x-2h)) / 2h

I just don't know how to write the code that will make the system of n non-linear equations to solve. I have a function that will solve them if I can get there...

any help or nudge in the right direction is appreciated

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