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- f(x) = x^2 - 2 ¤Î¶á»÷º¬¤òµá¤á¤ë¥×¥í¥°¥é¥à¤ò½ñ¤¤¤ÆÆ°¤«¤·¤Æ¤ß¤è¤¦¡¥
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- f(x) = 3x^2 + 1 + (log (Pi - x))^2/(Pi^4) ¤Ë¤Ä¤¤¤Æ¶á»÷º¬¤òµá¤á¤é¤ì¤ë¤À¤í¤¦¤«¡¢¥Á¥ã¥ì¥ó¥¸¤·¤Æ¤ß¤è¤¦¡¥ ¤¿¤Ö¤ó¡¢¤Á¤ç¤Ã¤ÈÆñ¤·¤¤¡¥
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2x^2 + y^2 - 1 = 0,
x - (¢å3)y = 0,
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- du/dt = u(1-u) ¤È¤¤¤¦Ã±½ã¤ÊÊýÄø¼°¤Î¶á»÷²ò¤òµá¤á¤ë¥×¥í¥°¥é¥à¤ò½ñ¤¤¤ÆÆ°¤«¤·¤Æ¤ß¤è¤¦¡¥
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du/dt = (2-v)u,
dv/dt = (2u - 3)v,
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u = u(x) ¤ËÂФ¹¤ë 1¼¡¸µ¶³¦ÃÍÌäÂê
u_{xx} = -C, (C > 0, const.) in [0,L],
u(0) = 0, u(L) = 1,
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u_t = u_{xx} in [0,L],
u(0) = 0, u(L) = 1,
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d^2 w/dt^2 = - a sin(w),
¤¿¤À¤·¡¢w = w(t) ¤Ï¿¶¤ê»Ò¤Î±ôľÊý¸þ¤«¤é¤Î³ÑÅÙ¡¢ a := g/l, g:½ÅÎϲîÅÙ¡¢l: ¿¶¤ê»Ò¤Î»å¤ÎŤµ. - Ç®³È»¶ÊýÄø¼°¤ËÂФ·¤Æ¡¢»þ´Ö¶õ´Ö¶¦¤ËÂоΤʺ¹Ê¬²òË¡(Crank-Nicolson ¥¹¥¡¼¥à¤È¸Æ¤Ð¤ì¤ë)
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¢é u^2 dx
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¢é (u_x)^2 dx
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¤Ê¤ª¡¢¤½¤Î Crank-Nicolson ¥¹¥¡¼¥à¤Ï°Ê²¼¤Î¤È¤ª¤ê¡¥
{ u_k^(n+1) - u_k^(n) }/¦¤t = { u_{k-1}^(n+1) - 2u_k^(n+1) + u_{k+1}^(n+1) + u_{k-1}^(n) - 2u_k^(n) + u_{k+1}^(n)} /(2¦¤x^2), for n = 0,1,2,..., k = 1,2,...,N-1,
u_0^(n) = 0, u_N^(n) = 1,
¤¿¤À¤·¡¢u_k^(n) ¤Ï u(k¦¤x, n¦¤t) ¤Î¶á»÷ÃÍ, N = L/¦¤x.