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

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The discussion focuses on implementing the Runge-Kutta 4 (RK4) method for solving a system of second-order differential equations related to boundary value problems. The equations provided are X''[T]=K (1-L) sinB and Y''[T]=K (1-L) cosB - 1, with specific boundary conditions for L, B, X, and Y. The solution requires transforming the second-order equations into first-order systems, allowing the application of the RK4 method to handle the resulting independent equations effectively. The discussion emphasizes the necessity of understanding the conversion process and the structure of the RK4 algorithm for successful implementation.

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  • Understanding of second-order differential equations
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  • Study the process of converting second-order differential equations to first-order systems
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Mathematicians, physicists, and engineers working on numerical solutions to differential equations, particularly those dealing with boundary value problems and the application of the Runge-Kutta method.

shaqychan
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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,
 
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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?
 
[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.

need more help "www.mathworld.com" greatest site ever =]
 

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