BVP for $y'' - 2y^3 = 0$ where $h= 0.25 , y(-1) = 0.5 y(0) = 0.5 , [-1.0]$ by using finite difference method

Question

find BVP for $y'' - 2y^3 = 0$ where $h= 0.25 , y(-1) = 0.5 y(0) = 0.5 , [-1.0]$ by using finite difference method.

I have been trying to solve this but I got a system of equations where my variables are more than my equations. Any help please... and can I use Gaussian elimination.

Answer 1

As mentioned in the comments, the finite difference discretization leads to the nonlinear system $$ \begin{cases} y_2-2y_1+\frac 12 -2h^2y_1^3=0\\ y_3-2y_2+y_1-2h^2y_2^3=0\\ \frac 12-2y_3+y_2-2h^2y_3^3=0 \end{cases}, $$

which you can solve by a numerical method of your preference. If you use Newton's method starting from $(0,0,0)$, you'll get 6 correct digits after 5 iterations.