Shooting method Guide, Meaning , Facts, Information and Description
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.)
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