How do I use RungeKutta 4/shooting method for this problem?

[shaqychan]

X''[T]=K (1-L) sinB
Y''[T]=K (1-L) cosB -1
X[T]=sinB0+L sinB
Y[T]=-cosB0+L cosB

Boundary conditions (B0, U, V are constants)
L[0]=L[End]=1
B[0]=-B0, B[End]=B0
X'[0]=X'[End]=U
Y'[0]=-V, Y'[End]=V

I don't know how to set up RungeKutta for this? Please help if you can.
Thx,

 

[LeBrad]

Your notation/equations confuse me. Are B and L functions of T? What is K? And is there a physical meaning to your problem/equations?

 

[neurocomp2003]

[0] y' = f(t,y) (1st order) is what RK4 solves as a system.(multiple equations)
[1] y" = f(t,y,y') (2nd order)is what you have.
[2] your eq'ns can be arranged to be independent set(x,y independent of each other)

step1->make the 2 independent systems
step2->you need to convert these 2 systems of 2nd Order into 1st order systems.
step3->then you use RK4 on all the equations you have. Should be 2 systems of 2eq'n = 4.


RK4 is a summation series so your B.Cs will give the limits to which you some over.

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