Hoʻolālā no ka hoʻoponopono ʻana i nā kaulike nonlinear
ʻO ka hoʻohālikelike nonlinear kahi hoʻohālikelike i hana ʻole i kahi laina pololei ke kaha kiʻi ʻia. ʻOi aku ka paʻakikī o kēia mau hoʻohālikelike ma mua o nā hoʻohālikelike linear a ʻaʻole hiki ke hoʻoponopono ʻia ma ke ʻano loiloi me ka hoʻohana ʻana i nā ʻano hana maʻamau e like me ka hoʻohui maʻalahi, ka hoʻemi ʻana, ka hoʻonui ʻana, a i ʻole ka mahele ʻana.
He mea nui ka hoʻomaopopo ʻana pehea e hoʻoponopono ai i nā kaulike nonlinear ma nā ʻano ʻepekema he nui, me ke kino, ke kemika, ka biology, ka hoʻokele waiwai, a me ka ʻenekinia. E kūkākūkā kēia ʻatikala i kekahi mau hoʻolālā kaulana no ka hoʻoponopono ʻana i nā kaulike nonlinear, me nā ʻano helu a me nā ʻano loiloi.
Pendahuluan
I nā hihia he nui, puka mai nā kaulike nonlinear ma ke ʻano he kumu hoʻohālike no nā hanana paʻakikī. No ka laʻana, i loko o nā dynamics fluid, nā hopena kemika, a i ʻole nā ʻōnaehana hoʻokele waiwai, ʻoi aku ka pololei a me ka pili o nā kumu hoʻohālike nonlinear. Eia nō naʻe, ʻo ka paʻakikī o nā kaulike nonlinear e paʻakikī ai ke hoʻoponopono me ka hoʻohana ʻana i nā ʻano maʻalahi a i ʻole ka algebra kumu. No laila, ua hoʻomohala ʻia nā ʻano hana a me nā ʻenehana like ʻole e hoʻoponopono i kēia pilikia.
Ke ʻAno Hana Hou
1. Ke ʻano hana ʻo Newton-Raphson
ʻO ke ʻano hana Newton-Raphson kekahi o nā ʻano hana iterative kaulana loa no ka loaʻa ʻana o nā aʻa o nā kaulike nonlinear. No kahi hana \( f(x) = 0 \), hoʻohana kēia ʻano hana i kahi ala iterative e hoʻokokoke i ka hopena me ke ʻano hana:
\[ x_{n+1} = x_n – \frac{f(x_n)}{f'(x_n)} \]
Maanei, ʻo \( f'(x_n) \) ka derivative mua o ka hana \( f \) ma ke kiko \( x_n \). He wikiwiki a hui pū kēia ʻano hana ke hoʻohana ʻia kokoke i nā aʻa o ka hopena, inā ʻaʻole hiki i ka derivative o ka hana ke hoʻokokoke i ka zero.
Laʻana hoʻokō:
1. E koho i ke kiko hoʻomaka \( x_0 \).
2. E helu iā \( f(x_0) \) a me \( f'(x_0) \).
3. E hoʻohana i ke ʻano hana hou e loaʻa ai \( x_1 \).
4. E hana hou i nā ʻanuʻu 2 a me 3 a hiki i ka waiwai o \( x_{n+1} \) e hoʻokokoke aku i ke aʻa me ke ahonui i makemake ʻia.
Eia nō naʻe, he nāwaliwali ko ke ʻano hana ʻo Newton-Raphson, ʻoiai inā koho ʻoe i kahi hoʻomaka e mamao loa ana mai ke aʻa maoli a inā kokoke ka derivative mua i ka ʻole.
2. Ke ʻAno Hoʻokaʻawale
ʻO ke ʻano hana Secant kahi hoʻololi o ke ʻano hana Newton-Raphson ʻaʻole pono ka derivative mua. ʻO ke ʻano hana iterative:
\[ x_{n+1} = x_n – \frac{f(x_n)(x_n – x_{n-1})}{f(x_n) – f(x_{n-1})} \]
ʻO ka pōmaikaʻi o kēia ʻano hana, ʻo ia ka hoʻopau ʻana i ka pono e helu i nā derivatives, kahi mea hiki ke paʻakikī. Eia nō naʻe, ma ke ʻano laulā, ʻoi aku ka lohi o kēia ʻano hana ma mua o Newton-Raphson.
3. Ke ʻAno Hoʻokaʻawale
ʻO ke ʻano Bisection kahi ʻano kumu e hōʻoiaʻiʻo ana i ka hui ʻana, akā ma kahi wikiwiki iteration lohi. Hilinaʻi kēia ʻano hana i ka Theorem a Bolzano e ʻōlelo ana inā he hana \( f(x) \) e hoʻomau ʻia ana i loko o ka manawa \([a, b]\) a me \( f(a) \cdot f(b) < 0 \), a laila aia ma ka liʻiliʻi hoʻokahi kiko \( c \) kahi \( f(c) = 0 \). ʻO nā ʻanuʻu: 1. E koho i ʻelua mau wahi hoʻomaka \( a \) a me \( b \) i hiki ai iā \( f(a) \cdot f(b) < 0 \). 2. E huli i ke kikowaena \( c = \frac{a + b}{2} \). 3. E huli iā \( f(c) \). 4. Inā \( f(c) = 0 \), a laila ʻo \( c \) he aʻa. 5. Inā \( f(c) \neq 0 \), e nānā i ka hōʻailona o \( f(a) \cdot f(c) \). Inā he maikaʻi ʻole, e pani iā \( b \) me \( c \); inā he maikaʻi, e pani iā \( a \) me \( c \). 6. E hana hou i ke kaʻina hana a hiki i ka liʻiliʻi o ka manawa [a, b].
He paʻa loa kēia ʻano hana a loaʻa mau nā aʻa i loko o ka wā i hāʻawi ʻia akā hiki ke lohi i ke ʻano o ka hui ʻana. Nā Hana Loiloi Pili nā ʻano hana loiloi i ka noʻonoʻo makemakika hohonu a me nā hana algebraic e ʻimi i nā hopena i nā kaulike nonlinear. 1. Hoʻololi a me ka Hoʻololi Hiki ke hoʻomaʻalahi ʻia kekahi mau kaulike nonlinear ma ka hoʻonohonoho hou ʻana i nā loli a i ʻole ka hana ʻana i nā pani. Hiki i kēia mau hoʻololi loli ke hoʻololi i ka kaulike nonlinear i kahi ʻano i maʻalahi ke hoʻoponopono. 2. Factorization Hiki ke hoʻohui pinepine ʻia nā kaulike kiʻekiʻe i loko o kahi huahana o nā kaulike linear a quadratic paha. No ka laʻana, hiki ke hoʻomaʻalahi ʻia kahi kaulike polynomial nonlinear ma ka loaʻa ʻana o kona mau aʻa factored. 3. Series ʻO ka hoʻohana ʻana i ka moʻo Taylor a i ʻole nā moʻo Fourier i kekahi manawa hiki ke kōkua i ka hoʻoponopono ʻana a i ʻole ka hoʻokokoke ʻana i ka hopena o kahi kaulike nonlinear. Pili kēia ʻano hana i ka hoʻonui ʻana i ka hana ma ke ʻano moʻo a laila e ʻokiʻoki iā ia i kahi ʻano e hiki ai i kahi hopena kokoke. Nā Hana Hoʻokolohua 1. Algorithm Genetic ʻO ka Algorithm Genetic kahi ʻano hoʻonui evolutionary a me ka simulation-based e hoʻoponopono ai i nā kaulike nonlinear. Pili kēia ʻano hana i ke koho ʻana, ke crossover, a me nā kaʻina hana mutation e ʻike i nā hopena kūpono a kokoke paha i ka maikaʻi loa. 2. Simulated Annealing ʻO ka Simulated Annealing kahi ʻenehana hoʻonui e hoʻohālike ana i ke kaʻina hana hoʻoluʻu i ka metallurgy. He mea pono loa kēia ʻano hana no ka loaʻa ʻana o ka palena iki o nā hana nonlinear. Nā Hana Kiʻi I kekahi manawa hiki i ka graphing i kahi kaulike nonlinear ke hāʻawi i ka ʻike nui i ke ʻano o ka hopena. ʻO ka hoʻolālā ʻana i ka hana a me ka nānā ʻana i nā x-intercepts hiki ke kōkua i ka hoʻomaopopo ʻana i ke ʻano o ka hopena. Laʻana Hihia 1. Nā Kaulike a Kepler I loko o nā mechanics lani, pili nā kānāwai o Kepler i nā kaulike nonlinear i hiki ʻole ke hoʻoponopono pololei ʻia. Hoʻohana pinepine ʻia ke ʻano Newton-Raphson e hoʻoponopono i kēia mau kaulike. 2. Pena ʻAʻole Newtonian I loko o nā mechanics fluid no nā wai ʻaʻole Newtonian, pili nā hiʻohiʻona makemakika i nā kaulike nonlinear paʻakikī a hoʻoponopono pinepine ʻia me ka hoʻohana ʻana i nā ʻano helu e like me ke ʻano Runge-Kutta. Hopena ʻO ka hoʻoponopono ʻana i nā kaulike nonlinear he pilikia nui ia ma nā ʻano like ʻole. ʻO nā ʻano hana Newton-Raphson, Secant, a me Bisection kekahi o nā ʻano hana helu i hoʻohana pinepine ʻia. Hāʻawi pū nā koho loiloi a me nā ʻano hana hoʻohālike i nā ʻano like ʻole e hoʻoponopono ai i nā paʻakikī o nā kaulike nonlinear. ʻO ke koho ʻana o ke ʻano kūpono e pili ana i ke ʻano o ka hoohalike a me ka pololei a me ka pono e pono ai no ka hoʻoponopono ʻana.