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Posted by helloktk
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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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Posted by helloktk
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