鍙嬫儏鎻愮ず锛氭湰绔欐彁渚涘叏鍦�(gu贸)400澶氭墍楂樼瓑闄㈡牎鎷涙敹纰╁+銆佸崥澹爺绌剁敓鍏ュ(xu茅)鑰冭│姝峰勾鑰冪爺鐪熼銆佽€冨崥鐪熼銆佺瓟妗�锛岄儴鍒嗗(xu茅)鏍℃洿鏂拌嚦2012骞�锛�2013骞达紱鍧囨彁渚涙敹璨�(f猫i)涓嬭級銆� 涓嬭級娴佺▼锛� 鑰冪爺鐪熼 榛�(di菐n)鎿娾€�鑰冪爺瑭﹀嵎鈥濃€濅笅杓�; 鑰冨崥鐪熼 榛�(di菐n)鎿娾€�鑰冨崥瑭﹀嵎搴�(k霉)鈥� 涓嬭級
銆婅▓(j矛)绠楁柟娉曘€嬭€冪爺寰�(f霉)瑭﹀ぇ缍卞拰鍙冭€冩浉鐩�
鍙冭€冩暀鏉愶細銆婃暩(sh霉)鍊煎垎鏋愩€�(绗洓鐗�)锛屾潕鎱舵彋(y谩ng)锛岀帇鑳借秴锛屾槗澶х京绶紝鑿腑绉戞妧澶у(xu茅)鍑虹増绀�
鍙冭€冪敤鏇革細銆婃暩(sh霉)鍊煎垎鏋愬熀绀�(ch菙)銆�锛屽悓婵�(j矛)澶у(xu茅)瑷�(j矛)绠楁暩(sh霉)瀛�(xu茅)鏁欑爺瀹ょ法锛屽悓婵�(j矛)澶у(xu茅)鍑虹増绀�
銆婃暩(sh霉)鍊煎垎鏋愮啊(ji菐n)鏄庢暀绋嬨€�(淇▊鐗�)锛� 鐜嬭兘瓒呯法钁�锛岃彲涓鎶€澶у(xu茅)鍑虹増绀�
瑾茬▼鐨勫熀鏈収(n猫i)瀹硅姹�
1銆佷簡瑙f暩(sh霉)鍊艰▓(j矛)绠楁柟娉曠殑灏�(du矛)璞″拰鐗归粸(di菐n)锛屼簡瑙h宸殑渚嗘簮锛岀悊瑙h宸殑鐩搁棞(gu膩n)姒傚康锛岀煡閬撴暩(sh霉)鍊艰▓(j矛)绠楁噳(y墨ng)娉ㄦ剰鐨勪竴浜涘晱椤�銆�
2銆佹彃鍊艰垏鏇茬窔鎿悎锛氱悊瑙f彃鍊肩殑鍩烘湰姒傚康锛屾帉鎻℃媺鏍兼湕鏃ワ紙Lagrange锛夋彃鍊兼硶, 鐔熺反浣跨敤鎷夋牸鏈楁棩鎻掑€煎叕寮忥紝浜嗚В鐗涢爴(Newton)鎻掑€兼硶锛岀煡閬撳焹鐖剧背鐗�(Hermite) 鎻掑€兼硶銆佹浜ゅ闋�(xi脿ng)寮忓強鏈€浣冲钩鏂归€艰繎銆傛帉鎻℃洸绶氭摤鍚堢殑鏈€灏忎簩涔樻硶銆�
3銆佹暩(sh霉)鍊肩⿳鍒嗗拰鏁�(sh霉)鍊煎井鍒嗭細浜嗚В姗�(j墨)姊版眰绌嶅叕寮忕殑鍩烘湰鎬濇兂锛屾帉鎻$墰闋�-鏌壒鏂叕寮�锛岀啛绶存帉鎻℃褰㈠叕寮忋€佽緵鐢敓鍏紡鍙婂京(f霉)鍚堢殑姊舰鍏紡鍜岃畩姝ラ暦(zh菐ng)鐨勬褰㈠叕寮�锛屾帉鎻¢緧璨濇牸(Romberg) 姹傜⿳绠楁硶锛屼簡瑙i珮鏂�(Gauss)姹傜⿳鏂规硶,鐞嗚В楂樻柉(Gauss)姹傜⿳鏂规硶鐨勬€濇兂锛岀悊瑙f暩(sh霉)鍊煎井鍒嗙殑鍩烘湰鎬濇兂鍜屾柟娉�.
4銆� 闈炵窔鎬ф柟绋嬬殑鏁�(sh霉)鍊艰В娉曪細鎺屾彙瑙i潪绶氭€ф柟绋嬬殑浜屽垎娉曪紝鐞嗚В杩唬娉曠殑鍩烘湰鎬濇兂鍙婃柟娉�锛屼簡瑙h凯浠f硶鐨勬敹鏂傞殠鐨勬蹇靛強鍔犻€熻凯浠g殑鏂规硶锛屾帉鎻$墰闋擄紙Newton锛夊垏绶氭硶锛屼簡瑙e鸡鎴硶銆�
5銆� 绶氭€т唬鏁�(sh霉)鏂圭▼绲勭殑鏁�(sh霉)鍊艰В娉曪細鎺屾彙楂樻柉锛圙auss锛夋秷鍘绘硶锛岀悊瑙d笁瑙掑垎瑙�锛屼簡瑙h拷瓒曟硶锛屼簡瑙e悜閲忚垏鐭╅櫍鐨勪笁绋寖鏁�(sh霉)鍙婃柟绋嬬祫鐨勬€ф厠(t脿i)鑸囨浠舵暩(sh霉)锛� 鎺屾彙闆呭彲姣旓紙Jacobi锛夎凯浠f硶锛岄珮鏂攢鈹€璩藉痉鐖撅紙Gauss-Seidel锛夎凯浠f硶銆備簡瑙h凯浠f敹鏂傜殑鍏呰姊濅欢锛岀煡閬撹秴鏉鹃Τ娉曘€�
6銆佸父寰垎鏂圭▼鍒濆€煎晱椤岀殑鏁�(sh霉)鍊艰В娉曪細鎺屾彙姝愭媺(Euler)娉曞強鏀归€�(j矛n)鐨勬瓙鎷�(Euler)鏂规硶锛屾帉鎻¢緧鏍尖攢鈹€搴�(k霉)濉�(Runge-Kutta)娉�锛屼簡瑙f埅?c谩i)鍡綻宸�锛岀┅(w臎n)瀹氭€э紝鏀舵杺鎬х殑鍚京锛屼簡瑙g窔鎬у姝ユ硶鐨勬蹇碉紝浜嗚В涓€闅庡井鍒嗘柟绋嬬祫鑸囬珮闅庡井鍒嗘柟绋嬬殑鏁�(sh霉)鍊艰В娉�銆�
鍏嶈铂(z茅)鑱叉槑锛氭湰鏂囩郴杞�(zhu菐n)杓夎嚜缍�(w菐ng)绲�(lu貌)锛屽鏈変镜鐘�锛岃珛(q菒ng)鑱�(li谩n)绯绘垜鍊戠珛鍗冲埅闄�锛屽彟锛氭湰鏂囧儏浠h〃浣滆€呭€�(g猫)浜鸿榛�(di菐n)锛岃垏鏈恫(w菐ng)绔欑劇闂�(gu膩n)銆傚叾鍘熷壍(chu脿ng)鎬т互鍙婃枃涓櫝杩版枃瀛楀拰鍏�(n猫i)瀹规湭缍�(j墨ng)鏈珯璀夊(sh铆)锛屽皪(du矛)鏈枃浠ュ強鍏朵腑鍏ㄩ儴鎴栬€呴儴鍒嗗収(n猫i)瀹�銆佹枃瀛楃殑鐪熷(sh铆)鎬�銆佸畬鏁存€с€佸強鏅�(sh铆)鎬ф湰绔欎笉浣滀换浣曚繚璀夋垨鎵胯锛岃珛(q菒ng)璁€鑰呭儏浣滃弮鑰冿紝骞惰珛(q菒ng)鑷鏍稿(sh铆)鐩搁棞(gu膩n)鍏�(n猫i)瀹�銆�
|