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Shooting Methods

Boundary value problems are ordinary differential equations with conditions imposed on the boundaries. We consider second order differential equations and the two condition on the boundaries can be pure (both on the positions or both on the derivatives) or mixed (one on the position and the other on the derivative). A shooting method reduces the solving of a boundary value problem to solving multiple initial value problems, starting with guesses for the missing initial condition. In case the boundary value problem is linear, then interpolation gives the correct solution after solving two initial value problems. To solve nonlinear boundary value problems, higher degree interpolation has to be applied.