# Two point boundary value problem NEW EXPLANATION ****

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I am trying to use the secant method to obtain a numerical solution to a two point boundary problem. Here is the differential equation - x' = f(t, x) = x + 0.09 * 2 + cos(10 t) and here is the boundary condition - x(0) + x(1) - 3.0 = 0 I also have the algorithm for the secant method which looks like this xk+1 = x - (f(xk)(xk - xk-1))/(f(xk) - f(xk-1)) Whereby k denotes the current iteration k-1 denotes the previous and k+1 denotes the next(I think). Also, f is the differential equation above (I think). Could somebody confirm that this is correct so far? Then I am asked, using 0.7 and 1.0 as initial guesses for the value of x(0) to find an approximation for x(0) (for x(t)) such that the boundary condition is satisfied to within a tolerance of 10-4. Could somebody explain what this tolerance of 10-4 means? Then I am instructed to used a fixed stepsize of 0.025 for t between 0 and 1. So am I to assume that I do the following: 1. Work out x(1) using the boundary condition and an intial guess (lets say 0.7). 2. Use x(0) and x(1) as x(k-1) and x(k) in the secant algorithm to calculate x(k+1). 3. Increment t by 0.025 and carry out step 2 again etc. Does this make sense to anyone? I can't figure what I am supposed to be doing here. Here is the actual assignment incase I was unclear anywhere. ************************************************ Construct a computer program that uses both the secant method and the Runge-Kutta method (that you developed in assignment #3) to obtain a numerical solution to the two-point boundary-value problem: x' = f(t,x) = x + 0.09 x 2 + cos(10 t) differential equation x(0) + x(1) - 3.0 = 0 boundary condition Starting with the initial guesses 0.7 and 1.0 for the (unknown) initial value, x(0), obtain an approximation to x(0) {for the final solution, x(t)} such that the boundary condition is satisfied to within a tolerance of 10-4 . Use a fixed stepsize of 0.025 (i.e., take 40 steps each time you integrate the differential equation from t=0 to t=1). Write your program so that the output shows the values of x(0), x(1), and x(0)+x(1)-3 (the error in satisfying the boundary condition) at the end of each iteration of the secant method. After the last iteration of the secant method, re-integrate from t=0 to t=1 and print out the solution for x(t) over the range [0,1]. ************************************************ Thanks for any help, I am completely dumbfounded by this one. Mark [Edited by - mrmrcoleman on February 28, 2006 10:02:52 AM]

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Er, this seems academic, something from school. gamedev is not an appropriate place to look for homework/schoolwork help, and this type of post is against the forum policy. See the Forum FAQ for more details.

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