Finding the Initial Point for Runge Kutta 4th Order

[sos 2011]

Hi guys

I have two points A and B (in 2 dimensions) and want to use runge kutta 4th order to give me points between these two points starting from A __> B (NOT B___> A). How can I choose the initial point then.

Cheers,

 

[HallsofIvy]

Perhaps I am misunderstanding but if you want a sequence of points going from A to B, then you would start at A. Take your initial point to be A.

 

[sos 2011]

If I have 3 points A,B,C and want to know the points between A and B, how can I force the runge kutta to go from A to B not anywhere? I think there is a relation formula can connect A and B and consider it as an initial point. Any idea?

 

[someperson05]

I don't quite understand what you are asking. Are you saying you have an interval
[A, B]
and you want to fill in the graph between these x values?

I don't see how your saying a Runge Kutta method would go "anywhere"? It has to follow the differential equations you have.

EDIT:
If I remember correctly, to apply Runge Kutta you start with the location of the given initial condition, and then iterate from there.

 

[EnumaElish]

I think the OP is asking about a boundary problem, such that the solution is "fixed" not only at the initial point A but also at the "boundary point" B. Generally speaking there is no numerical "formula" to ensure that an initial point A(i) is going to yield the solution that also goes through B. A useful theorem states that the mapping of the initial points A(1), A(2), ... to the corresponding sequence of points B(1), B(2), ... near B is continuous, so you should be able to approximate B to a high degree of precision by trying out different values of A. Also, if your diff. eq. is not singular at B then you can try a backward solution from B to A.