Shooting method for the boundary value problems: Maple

Physics/Research 2012. 8. 1. 16:14

 

 

 

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Shooting Method for Boundary Value Problem: Mathematica

Physics/Research 2012. 7. 28. 14:17

Mathematica에서 shooting method를 이용해서 비선형 미분방정식의 해를 구하자. 

\begin{align}f' &= \frac{1}{x} (1-a) f \\ a'&=- \frac{x}{2} f^2 (f^2-1) \end{align}

경계조건은 $f(0)=0$, $f(\infty)\to 0$, $a(0)=0$을 만족시켜야 한다. $x$가 증가하면 $f(x)$는 빠르게 $1$로 수렴하므로 오른쪽 경계조건은 $f(15)\to1$로 잡아도 충분하다. $x=0$에서의 apparent singularity를 Mathematica가 처리할 수 있도록 방정식을 변형시켜주어야 한다.

 

 

 

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Internet Resources for Shooting Methods for ODE's

Physics/Research 2010. 9. 4. 15:09

  1. Shooting Methods for 2-Point Boundary Value Problems  
    Jonathan Thornburg,  Max Planck Institut für Gravitationsphysik, Berlin, Germany
  2. Two Point Boundary Value Problems. Solution Methods.  
    R.D. Poshusta, Chemistry Dept., Washington State University, Pullman, WA
  3. The Shooting Method  
    Reza Fotouhi-Chahouki, Dept. of Mechanical Engineering, Univ. of Saskatchewan, Canada
  4. The Shooting Method for 2-Point BVP's  
    J. R. White, Chemical & Nuclear Engineering Dept., University of Massachusetts, Lowell, MA
  5. A Overview of the Shooting Method  
    Adept Scientific plc, Herts, SG6 1ZA, UK
  6. The Shooting Method  
    Juan Restrepo, Math. Dept, Univ. of Arizona, Tucson, AZ
  7. The Shooting Method, Nonlinear Case  
    Juan Restrepo, Math. Dept, Univ. of Arizona, Tucson, AZ
  8. Boundary Value Problems ... Shooting Method  
    Paul Heckbert, Computer Science Dept., Carnegie Mellon University, Pittsburgh PA
  9. Boundary Value problems ... Shooting methods  
    Jun Ni, Department of Mechanical Engineering, Department of Civil Engineering, The University of Iowa
  10. Shooting Method   
    Heinrich Kirchauer, Institute for Microelectronics, Technical University of Vienna
  11. Shooting  
    E. Bruce Pitman, Math. Depat. State University of New York, Buffalo, NY
  12. Shooting method     
    Stuart Dalziel, University of Cambridge, Cambridge, England    
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