The shooting method is a trial-and-error method. To solve a problem where the values of y are known at x0 and x„, the boundaries of the interval of interest, we set up the problem as though it were an initial-value problem, with two "knowns" given at the same boundary — for example, at x0- (See Figure 10-17 for an example of an initial-value problem of this type: the two knowns, shown in bold, are the value ofy at jc0 and a trial value of y' at jc0.) Using the trial value of y\ we calculate y for a suitable range of x values from x0 to xn, and compare the calculated value of y at xn with the known value. If the calculated value does not agree with the known value, we repeat the calculations with a different trial value of y\ until we calculate a value of y at the other boundary, x„, that agrees with the boundary value, hence the name "shooting method."
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