Expansion in time

We would also like to characterize the solution near a particular arbitrary time, say [Maple Math] . Substitute [Maple Math] and expand on [Maple Math] . For illustration, we look at just the second-order expansion.

long expression

[Maple Math]

[Maple Math]

As we can see, expansions of useful order will generate large expressions. However, the appearance of these expressions can be considerably simplified by converting to Fourier form. For example,

[Maple Math]

[Maple Math]
[Maple Math]
[Maple Math]
[Maple Math]
[Maple Math]
[Maple Math]
[Maple Math]
[Maple Math]
[Maple Math]

[Maple Math]

[Maple Math]