Numerical Methods

[Guest]

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Please tell me how to solve this problem. A File is attached.

[HallsofIvy]

This is very strange. Are you taking a course on "Differential Equations" and numerical solutions? If not, where did you get this problem? If yes, didn't you learn what "forward differencing", "backward differencing", and "central differencing" mean?

[HallsofIvy]

Using "analytical" rather than numerical methods, the general solution is [tex]\Phi(t)= Ae^t+ \frac{1}{2}t^2[/tex] and, with [tex]\Phi(0)= A= 1[/tex] so [tex]\phi(t)= e^t+ \frac{1}{2}t^2[/tex]. Use that to check your numerical answer,