Tugas 01 Numerik Lanjut.docx

TUGAS 01 METODA NUMERIS LANJUT DOSEN : MAS MERA Ph.D

BOBBY NEILZON 1620922016

MAGISTER TEKNIK SIPIL FAKULTAS TEKNIK UNIVERSITAS ANDALAS 2016

1. SolusiAnalisis 𝑎𝑥 3 + 𝑏𝑥 2 + 𝑐𝑥 + 𝑑 = 0 A=1, b=-5, c=-10, d=50 𝑥 3 − 5𝑥 2 − 10𝑥 + 50 = 0 𝑥 2 (𝑥 − 5) − 10(𝑥 − 5) (𝑥 2 − 10)(𝑥 − 5) (x+√10) (x-√10)(x-5) (-√10, √10, 5) 2. SolusiNumeris 𝑎𝑥 3 + 𝑏𝑥 2 + 𝑐𝑥 + 𝑑 = 0 𝑥 3 − 5𝑥 2 − 10𝑥 + 50 = 0 𝑥 3 = 5𝑥 2 + 10𝑥 − 50 𝑥 3 5𝑥 2 + 10𝑥 − 50 = 𝑥2 𝑥2 Persamaan 1 - - - 𝑥 = 5 +

10 𝑥

50

− 𝑥2

5𝑥 2 = 𝑥 3 − 10𝑥 + 50 𝑥

2

10

Persamaan 2 - - - 𝑥 = 5 − 𝑥 + 𝑥 2 10𝑥 = 𝑥 3 − 5𝑥 2 + 50 Persamaan 3 - - - 𝑥 =

𝑥 3 −5𝑥 2 +50 10

Persamaan 1 Xn Xn+1 Xn+1 - Xn 3 2.777778 -0.222222 2.77778 2.12000 -0.657778 2.12000 -1.40797 -3.527974 -1.40797 -27.32446 -25.916485 -27.32446 4.56706 31.891519 4.56706 4.79243 0.225375 4.79243 4.90963 0.117192 4.90963 4.96251 0.052881 4.96251 4.98478 0.022268 4.98478 4.99387 0.009097 4.99387 4.99754 0.003670 4.99754 4.99902 0.001473 4.99902 4.99961 0.000590 4.99961 4.99984 0.000236 4.99984 4.99994 0.000094 4.99994 4.99997 0.000038 4.99997 4.99999 0.000015 4.99999 5.00000 0.000006 5.00000 5.00000 0.000002

Xn 3 1.044444 2.852890 2.989673 3.060242 3.100225 3.123948 3.138384 3.147302 3.152859 3.156342 3.158532 3.159912 3.160783 3.161333 3.161680 3.161900 3.162039 3.162127 3.162182 3.162217 3.162239 3.162253 3.162262 3.162268 3.162272 3.162274 3.162275 3.162276 3.162277 3.162279

Persamaan 2 Xn+1 Xn+1 - Xn 1.044444 -1.95555556 2.852890 1.80844541 2.989673 0.13678292 3.060242 0.07056891 3.100225 0.03998375 3.123948 0.02372224 3.138384 0.01443668 3.147302 0.00891722 3.152859 0.00555753 3.156342 0.00348275 3.158532 0.00219001 3.159912 0.00138006 3.160783 0.00087083 3.161333 0.00054997 3.161680 0.00034751 3.161900 0.00021966 3.162039 0.00013887 3.162127 0.00008781 3.162182 0.00005553 3.162217 0.00003512 3.162239 0.00002221 3.162253 0.00001405 3.162262 0.00000888 3.162268 0.00000562 3.162272 0.00000355 3.162274 0.00000225 3.162275 0.00000142 3.162276 0.00000090 3.162277 0.00000057 3.162277 0.00000036 3.162279 -0.00000049

Xn 3 3.200000 3.156800 3.163180 3.162132 3.162301 3.162274 3.162278 3.162278 3.162278

Persamaan 3 Xn+1 3.200000 3.156800 3.163180 3.162132 3.162301 3.162274 3.162278 3.162278 3.162278 3.162278

Xn+1 - Xn 0.20000000 -0.04320000 0.00638001 -0.00104841 0.00016978 -0.00002756 0.00000447 -0.00000073 0.00000012 -0.00000002

Jadi hasilnya ( -3.162278, 3.162278, 5 ) ( √10, -√10, 5 )