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Abstract
We consider simple and multiple shooting methods for simple turning points, perturbed bifurcation points, cubic turning points and cusps in boundary value problems for ordinary differential equations. We discretize the original problem using the shooting technique to obtain a finite dimensional problem. A direct method is used for the characetrization and computation of simple turning points. Some suitable extension of this direct method is employed for the computation of bifurcation points and cubic turning points and cusps. Enough numerical examples are solved to demonstrate that the method is efficient.