Given the boundary value problem (primes denote differentiation w.r.t x):(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\begin{array}{l}

y'' = f(x,y,y') \\

y(a) = \alpha \\

y(b) = \beta \\

\end{array}[/tex]

the nonlinear shooting method may be implemented to solve the problem. A bisection algorithm may be used or, with a little more effort, Newton's method may be implemented (in which case one solves a fourth order, and not a second order, IVP - http://www.math.utah.edu/~pa/6620/shoot.pdf" [Broken]).

But what happens if the form of the boundary conditions changes to:

[tex]\begin{array}{l}

y'(a) = \alpha \\

y(b) = \beta \\

\end{array}[/tex]

Is one still justified in reducing the BVP to a 2nd order IVP, but this time with initial SLOPE fixed at [tex]y'(a) = \alpha [/tex] and then trying different values of [tex]y(a)[/tex] in order to achieve the condition [tex]y(b) = \beta [/tex]? (As opposed to varying initial slope to achieve second condition).

Furthermore, if this will indeed work, then a bisection method should be easy to implement, but what about adapting Newton's method for this case? Can anyone point me to an appropriate reference that discusses this matter?

Thank you! :-)

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# Nonlinear shooting (BVPs)

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