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G Tuorial xlc3.oc 7/ Noliear roblem i e e C (5 ie C ie Ex (5 i (53 e Differeial equaio for (5 i (53 C (54 (54 i (5 i Ex C e (55 (55 i (5 i e C. Ex C (56 Ex C C (57 Thi iffereial equaio cao be eaily ole, bu he iz-galerki meho ca be ue o fi ou a aroximae oluio. iz Galerki Meho (wih weihe reiual To aly he -G meho, he iffereial equaio mu be rereee i he form:
G Tuorial xlc3.oc 8/, /, / ] x (58 where x i a liear or oliear oeraor f oly oe reiual i coiere he aume aroximae oluio mu be rereee i he form below y( Yϕ ( (59 where ϕ i a fucio a he Y i a ajuable coa coefficie. Sice he aume oluio (59 oe o i eeral exacly aify he iffereial equaio (58, he exreio obaie by ubiui (59 io (59 i o loer ieically equal o zero:, /, / ] ε ( x (6 where ε( i he reiual ha meaure he error. Thi error i miimize if he followi reiual, calle he iz coiio, i aifie., /, / ] ϕ ( x (6 Thi roceure ie oe alebraic equaio i oe ukow. For circui how aboe, if.co( a rile elece, he he oluio for ca be aroximae by a ure DC olae wih he relaio below. ( (6 We hae oe ukow meai ha oe equaio i eee o fi ou The iz coiio will ie u hi eee equaio. By coieri reiual ol he ( ( λ ϕ λ λ (63 ( λ ϕ (64 [,,, /, / ] ϕ λ ( ( π ξ (65 Wih x efie i (57 ϕ efie i (64 λ ( ( co (66 efie i (6 ( G meho lea o ole he uique followi equaio From (65 [ co(,,, /, / ] ( λ ξ (67
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