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 Jun 4 awarded Notable Question Jul 2 awarded Curious May 12 awarded Popular Question May 12 awarded Popular Question Nov 26 awarded Popular Question Oct 15 awarded Popular Question May 22 awarded Popular Question May 10 revised Two-Point boundary value problem added 331 characters in body May 10 comment Two-Point boundary value problem Thanks @JitseNiesen The main part I was confused on is how to calculate the $f_j$. Could you see if what I've done is correct? I rearranged the equation and got $f_{j+1}(1-\frac{h}{2})+y_{j-1}(1+\frac{h}{2})+y_j(-2)=h^2f_j$. For example, $j=1 \Rightarrow f_{2}(1-\frac{h}{2})+y_{0}(1+\frac{h}{2})+y_1(-2)=h^2f_1$. So does $h^2f_1 = \frac{1}{36}\cdot(-\frac{1}{6})?$ And does $h^2f_2 = \frac{1}{36}\cdot(-\frac{2}{6})$? May 10 asked Two-Point boundary value problem May 9 asked Finite difference method for BVP (2nd order) May 9 comment 1st order ODE problem (forward euler) Ok, understood it now. Thanks again man, cheers! May 9 comment 2nd order ODE to 1st order ODE/Forward euler method Thanks, understood it. Much appreciated again. May 9 revised 2nd order ODE to 1st order ODE/Forward euler method Updated question May 9 comment 1st order ODE problem (forward euler) Quick question -- You wrote that $f(t_0,U^0) = u(0)$, does that mean $f(t_1,u^1) = u(1)$ and so forth for $n \in \mathbb{N}$? May 9 accepted 2nd order ODE to 1st order ODE/Forward euler method May 9 comment 2nd order ODE to 1st order ODE/Forward euler method Thanks @JohnathanGleason , I understood everything you did. I just have one more question -- How do I get from $f(t_0, W^0)= \left( \begin{array}{c} V^0 \\ 5\cdot 0 \cdot U^0 + \sin V^0 \end{array} \right) = \left( \begin{array}{c} 0 \\ 0 \end{array} \right)$? In particular, shouldnt $U^0 =1$? May 9 comment 1st order ODE problem (forward euler) Thanks Johnathan, great answer. :) May 9 accepted 1st order ODE problem (forward euler) May 9 asked 1st order ODE problem (forward euler)