shooting

When solving ODEs numerically, one usually uses methods like Runge-Kutta or Euler's method in which initial conditions are fully specified while ending conditions are unknown. The computer integrates the ODE (or system of ODEs) to a specified time (or location). However, this method cannot solve boundary value problems, since there is no way to enforce the far boundary condition.

Shooting solves this problem by repeatedly solving the ODE, changing the initial conditions to hit the desired far boundary condition, much like someone shooting at a target might adjust their aim. (For reasons I will not explain here, if there are n far boundary conditions to satisfy, there are also n free initial conditions that may be varied at will.)

Typical methods of adjusting the initial condition are bisection and Newton's method. A mathematician would think of shooting as finding the root of the function:

g(initial conditions) = f(t₁; initial conditions) - f₁

where f(t₁) is the computed far boundary condition, and f₁ is the desired far boundary condition. For most problems of interest, this is a transcendental equation, which cannot be solved algebraically.

Shoot"ing, n.

1.

The act of one who, or that which, shoots; as, the shooting of an archery club; the shooting of rays of light.

2.

A wounding or killing with a firearm; specifically Sporting, the killing of game; as, a week of shooting.

3.

A sensation of darting pain; as, a shooting in one's head.

© Webster 1913.

Shoot"ing, a.

Of or pertaining to shooting; for shooting; darting.

Shooting board Joinery, a fixture used in planing or shooting the edge of a board, by means of which the plane is guided and the board held true. -- Shooting box, a small house in the country for use in the shooting season. Prof. Wilson. -- Shooting gallery, a range, usually covered, with targets for practice with firearms.<-- [Slang] a place, often a building or neighborhood, where addicts "shoot up" drugs. --> -- Shooting iron, a firearm. [Slang, U.S.] -- Shooting star. (a) Astron. A starlike, luminous meteor, that, appearing suddenly, darts quickly across some portion of the sky, and then as suddenly disappears, leaving sometimes, for a few seconds, a luminous train, -- called also falling star. Shooting stars are small cosmical bodies which encounter the earth in its annual revolution, and which become visible by coming with planetary velocity into the upper regions of the atmosphere. At certain periods, as on the 13th of November and 10th of August, they appear for a few hours in great numbers, apparently diverging from some point in the heavens, such displays being known as meteoric showers, or star showers. These bodies, before encountering the earth, were moving in orbits closely allied to the orbits of comets. See Leonids, Perseids. (b) Bot. The American cowslip (Dodecatheon Meadia). See under Cowslip. -- Shooting stick Print., a tapering piece of wood or iron, used by printers to drive up the quoins in the chase. Hansard.

© Webster 1913.