In numerical analysis, the shooting method is a method for solving a boundary value problem by reducing it to an initial value problem. It involves finding solutions to the initial value problem for different initial conditions until one finds the solution that also satisfies the boundary conditions of the boundary value problem.

This method is called the shooting method because someone shooting at a target will adjust their next shot based where their previous shot landed. Use the Euler method with a step length of h = 0.2 and the shooting method to solve the following boundary value problem. y ″ − y ′ − y = 0, y (0) = 0, y (1) = 2. 5.2.1.

The Shooting Methods¶ The shooting methods are developed with the goal of transforming the ODE boundary value problems to an equivalent initial value problems, then we can solve it using the methods we learned from the previous chapter.

The shooting method algorithm is: Guess a value of the missing initial condition; in this case, that is \(y'(0)\) . Integrate the ODE like an initial-value problem, using our existing numerical methods, to get the given boundary condition(s); in this case, that is \(y(L)\) .

Dec 23, 2009 · The shooting method uses the same methods that were used in solving initial value problems. This is done by assuming initial values that would have been given if the ordinary differential equation were an initial value problem.

"Shooting" Method. The shooting method works by considering the boundary conditions as a multivariate function of initial conditions at some point, reducing the boundary value problem to finding the initial conditions that give a root.

This method of solving BVPs is called the shooting method, because you guess initial conditions and shoot over to other values to check whether they work or now. The key steps are: You have to be able to solve the IVP first, assuming you know the initial conditions.

Apply the shooting method to the falling object problem above, use Y 1 = 10 and Y 2 = 14 for the values for y 0 (0). You may use the exact solution instead of a numerical solver.

The Shooting Method for Boundary Value Problems Consider a boundary value problem of the form y00= f(x;y;y0); a x b; y(a) = ; y(b) = : (3.1) One natural way to approach this problem is to study the initial value problem (IVP) associated with this di erential equation: y00= f(x;y;y0); a x b; y(a) = ; y0(a) = t: (3.2)

Also, the shooting method can be used with IVPs of order higher than the second. For example, consider the BVP x3y′′′ +xy′ −y = −3+lnx, y(a) = α, y′(b) = β, y′′(b) = γ. (7.25) As in the previous example, denote y1 = y, y2 = y′, y3 = y′′ and rewrite the BVP (7.25) in …