In numerical analysis, the shooting method is a method for solving a boundary value problem by reducing it to the solution of an initial value problem. The following exposition may be clarified by this illustration of the shooting method.

For a boundary value problem of a second-order ordinary differential equation, the method is stated as follows. Let

be the boundary value problem. Let y(t₁; a) denote the solution of the initial value problem

Define the function F(a) as the difference between y(t₁; a) and the specified boundary value y₁.

If the boundary value problem has a solution, then F has a root, and that root is just the value of y'(t₀) which yields a solution y(t) of the boundary value problem.

The usual methods for finding roots may be employed here, such as the bisection method or Newton's method.

References

• Josef Stoer and Roland Bulirsch. Introduction to Numerical Analysis. New York: Springer-Verlag, 1980. (See Section 7.3.)