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## Main Question or Discussion Point

Is there a numerical method for finding solutions to 2nd order non-homogeneous differential equations? Thanks.

- Thread starter qspeechc
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Is there a numerical method for finding solutions to 2nd order non-homogeneous differential equations? Thanks.

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To solve a DE numerically you need not only the differential equations themselves but also information about the state. Initial value techniques are used in the case that the full state is known at some point in the domain. Boundary value techniques (much harder) are used in the case where only parts of the state are known, but at multiple points in the domain.

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HallsofIvy

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If, for example, you have the second order equation, Y"(x)= f(x, Y, Y'), you could let U(x)= Y' so that your equation becomes U'= f(x, Y, U). Because that equation still involves Y, you need two equations: U'= f(x,Y,U) and Y'= U. Now run two

For example, if you are given Y"= f(x,Y,Y') with initial conditions Y(x

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So, iffin I is understannin correkly, first find

U'= f(x,Y,U)

numerically, then from Y'= U find Y?

U'= f(x,Y,U)

numerically, then from Y'= U find Y?

HallsofIvy

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Ah, I think I get it. Probably not. Thank you HallsofIvy

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