What is Shooting method: Definition and 21 Discussions

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. In layman's terms, one "shoots" out trajectories in different directions from one boundary until one finds the trajectory that "hits" the other boundary condition. The following exposition may be clarified by this illustration of the shooting method.

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  1. patric44

    Non linear BVP using a shooting algoritm with MATLAB?

    hi guys i was trying to use this shooting algorithm from Xue and Chen Scientific Computing with MATLAB book : to solve this non linear temperature distribution problem : i checked my Matlab function multiple times but i am keep getting a nonsense graph for the temperature , can someone cheak...
  2. patric44

    Temperature Distribution of Current Carrying Wire in Matlab

    hi guys i was trying to solve this non linear ode using the shooting algorithm in Matlab : i am not sure how to solve it using the normal shooting algorithm i have , since no other boundary at x = L/2 was given to check the shooting ?! function dTdx = bar_temp(x,y) k = 72; h = 2000; epsilon =...
  3. B

    Comp Sci [C++] Schrodinger equation solver and nuclear density

    Hi everybody! I need to compute a C++ program for solve Schrodinger equation and calculate nuclear density. My nucleus is made up of only neutrons immersed in a potential of a harmonic oscillator. Schrodinger equation is: $$[-\frac{\hbar^2}{2m}\triangledown^2+V_{HO}(r)]\psi=E\psi$$ with...
  4. RamosPinto

    I Two point boundary problem - Shooting method

    I'm currently trying to solve the following two-point boundary problem by means of the shooting method: To clarify, I'm investigating the optimal route of aerial/marine vehicles from one point to another point, considering a flow field. * The starting and ending locations are set as x0, y0...
  5. Bassa

    "Shooting Method" for simulating a Particle in an Infinite Square Well

    Hello! I am trying to write a program that solves the Schrodinger Equation for a particle in an infinite square well. I did a lot of research regarding the methods that could be used to accomplish this. I am writing this program in Matlab. The method I am using is called the Shooting Method. In...
  6. S

    Boundary conditions shooting method

    I am trying to solve the differential equation ##\frac{d^{2}y}{dr^2}+(\frac{1}{r}+1)y=0## with the boundary conditions ##y(r) \rightarrow r \frac{dy}{dr}(0)## as ##r \rightarrow 0## and ##y(r) \rightarrow \sin(kr+\delta)## as ##r \rightarrow \infty##. I know that the shooting method is the...
  7. S

    Solving an ODE using shooting method

    Homework Statement I have been trying to solve the following nonlinear ordinary differential equation: ##-\Phi''-\frac{3}{r}\Phi'+\Phi-\frac{3}{2}\Phi^{2}+\frac{\alpha}{2}\Phi^{3}=0## with boundary conditions ##\Phi'(0)=0,\Phi(\infty)=0.##Homework Equations My solution is supposed to...
  8. electronic engineer

    How to Solve a Shooting Method Problem with Specific Boundary Conditions?

    Hello, can anyone give me the general instructions of solving shooting method problem: dy1/dx=-y1^2*y2 dy2/dx=y1*y2^2 with the boundary conditions: y1(0)=1, y2(1)=2
  9. S

    Solving an ODE using shooting method

    Hi, I am trying to solve the following ODE for my maths project: ## y'' = \frac{\alpha}{2}y^3 - \frac{3}{2}y^2 + y - \frac{3}{x} y'## under the following boundary conditions: ## y'(0) = 0 ## ## y(x) \rightarrow y \_ \equiv 0\ \text{as}\ x \rightarrow \infty ## As a first step, I converted...
  10. H

    Shooting Method to solve Blasius equation

    Hello all, I'm trying to write a bit of Matlab to solve the Blasius Equation f*f'' + f''' = 0, where at eta = 0, f' = 0, and at eta = infinity, f' = 1. What I have so far is below...I'm a bit rusty. Two specific questions: 1. I'm trying to drive y2 to the b.c. of 1, however my loop...
  11. S

    Shooting method for non-linear equation

    shooting method for non-linear equation(urgent) Homework Statement for shooting method , in non-linear equation, we're find $$t_{k}=t_{k-1}-\frac{[y(b,t_{k-1})-β](t_{k-1}-t_{k-2})}{y(b,t_{k-1})-y(b,t_{k-2})}$$ but how can we find the $$y(b,t_{k})$$ ? I am suppose to use Euler method for...
  12. J

    MATLAB Solving System of Equations w/MATLAB Shooting Method

    Hi all, I'm looking to solve the following system of equations with boundary conditions using the shooting method in MATLAB: F''=F^2-G^2+F'H G''=2FG+G'H H'=-2F along with the conditions F(0)=0, G(0)=1, H(0)=0, F(infinity)=0, G(infinity)=0. I've found the solution using the...
  13. P

    Applying shooting method to 4nd two point value boundary problem

    Hi, I was wondering if you can apply shooting method to a 4nd differential eq. two point value boundary problem, specifically I want to use this method to solve Euler-Bernoulli eq. EI y(4)(x)=f(x), y(0)=0,y'(0)=0,y(L)=0,y'(L)=0. Normally, if you have a 2nd order two point value...
  14. T

    Need Help Understanding Shooting Method

    I'm trying to solve a set of differential equations that all depend on a parameter, κ. I can use the system of ODEs to reduce the four equations into one second order differential equation, for y[x;κ]. I've seen certain tricks to solving equations such as d^2y/dx^2 = κ y[x].But I can not put my...
  15. P

    Shooting Method Boundary Problem

    Homework Statement y"+xy'=cos(2x), y(0)=1, y'(5)+2y(5)=10 Homework Equations The Attempt at a Solution I am trying to solve this using matlab. I split the 2nd order d.e. into 2 first order d.e.'s. I set y1=y, and y2= dy/dx. Thus dy1/dx=y2 and dy2/dx= cos(2x)-x*y2. Then dy/dt=...
  16. H

    MATLAB Matlab programming using shooting method, Euler and Runge Ketta methods

    I need help to solve this coursework: MATLAB PROGRAMMING COURSEWORK OBJECTIVES:  Learn to solve engineering problems using MATLAB  Write Euler and Runge-Kutta initial-value ODE solvers  Write a Shooting Method boundary-value ODE solver  Investigate the properties of the solvers ...
  17. M

    Shooting method vs. finite differences for BVP

    I am considering a second order ODE of the form y''(x) + f(x) y(x) = 0, with boundary conditions that y(x) = 0 at plus/minus infinity. Note that f(x) is complex for my case. It seems that the standard techniques for numerically solving this problem are (a.) the finite difference method and...
  18. B

    Shooting method and a shock wave (discontinuity at the inner boundary condition)

    I've done searching on the topic, and I really don't know where else to turn, so here it goes. I hope somebody can point me in the right direction. I've been working on using a shooting method to solve the steady-state spherically symmetric fluid equations for an accreting plasma. Basically, it...
  19. D

    Initial Value Problems for Linear Shooting Method

    Homework Statement y''-by'=f(x) I have to "derive and submit the appropriate initial value problems (with initial conditions) for u(x) and v(x). Show me all 4 equations and initial conditions... " and I know you get u(x) and v(x) by solving ivp's for the original equation, one...
  20. C

    How exactly does the shooting method work?

    I have an assignment which requires using the shooting method, but the problem is, I've read numerous things on the internet about exactly how the shooting method works, and I still don't understand it. I was hoping that someone would be kind enough to explain to me the fundamentals of how it works.
  21. A

    Approximating k with Shooting Method and Euler's Method

    dy/dt = ky, where k is a constant. y|t=0 = 1; y|t=10 = 4 I need to approximate k using the shooting method and Euler's method... please help.. :) wat's the procedure to approximate k using the shooting method :confused: