Numerical Methods for Ordinary Dierential Equations Episode 4 doc
Numerical Methods for Ordinary Dierential Equations Episode 4 doc
... 1 1 2 1 1 2 1 2 − 1 12 2 5 12 2 3 − 1 12 1 24 3 3 8 19 24 − 5 24 1 24 − 19 720 4 251 720 323 360 − 11 30 53 360 − 19 720 3 160 5 95 288 142 7 144 0 − 133 240 241 720 − 173 144 0 3 160 − 863 6 048 0 6 19087 6 048 0 2713 2520 − 1 548 7 20160 586 945 − 6737 20160 263 2520 − 863 6 048 0 275 241 92 7 5257 17280 139 849 120960 − 45 11 44 80 123133 120960 − 88 547 120960 1537...
Ngày tải lên: 13/08/2014, 05:21
Numerical Methods for Ordinary Dierential Equations Episode 1 docx
... stability 44 2 5 54 Methods with property F 44 5 555 Some non-stiff methods 44 6 556 Some stiff methods 44 7 557 Scale and modify for stability 44 8 558 Scale and modify for error estimation 45 0 References 45 3 Index ... stability 42 3 543 Almost Runge–Kutta methods 42 6 544 Third order, three-stage ARK methods 42 9 545 Fourth order, four-stage ARK methods 43 1...
Ngày tải lên: 13/08/2014, 05:21
Numerical Methods for Ordinary Dierential Equations Episode 2 docx
... comprising (124d), (124e), (124f) has been reduced, first to an index 1 formulation (124d), (124e), (124h), and then to an ordinary differential equation system (124d), (124e), (124i). Exercises ... z −1 n ,sothat z n + 1 z n = z 2 n−1 + 1 z 2 n−1 , 44 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS Exercises 13 13.1 Write the difference equation given by (134e) in the form z...
Ngày tải lên: 13/08/2014, 05:21
Numerical Methods for Ordinary Dierential Equations Episode 5 docx
... 10 −5 4. 588 54 82 8 −9 1.02365 × 10 −5 4. 78350 137 8 −10 2.15123 × 10 −6 4. 75 845 228 8 −11 4. 5 343 6 × 10 −7 4. 744 29 382 8 −12 9.57567 × 10 −8 4. 73529 642 8 −13 2.01165 × 10 −8 4. 76011 1078 8 − 14 4.22 848 ... 7 8 −1 1.226 74 3. 947 73 8 8 −2 3.3 040 1 × 10 −1 3.71289 8 8 −3 8.28328 × 10 −2 3.98876 10 8 4 2.33986 × 10 −2 3. 540 07 13 8 −5 4. 95205 × 10 −3 4. 725 04...
Ngày tải lên: 13/08/2014, 05:21
Numerical Methods for Ordinary Dierential Equations Episode 3 pot
... 113 040 0.0252×10 −10 4. 4125 40 256178.9889×10 −10 4. 1893 80 61150.2626×10 −10 4. 09 04 160 149 49.6176×10 −10 4. 044 2 320 3696.5967×10 −10 4. 0218 640 919.1362×10 −10 4. 0108 1280 229.1629×10 −10 4. 00 54 2560 57.21 34 10 −10 4. 0026 5120 ... 28 10 0.0181 748 9 −0.01737078 47 20 0.0089 848 3 −0.00878393 80 40 0.0 044 67 04 −0.0 044 1680 149 80 0.00222721 −0.0022 146 2 240...
Ngày tải lên: 13/08/2014, 05:21
Numerical Methods for Ordinary Dierential Equations Episode 6 ppsx
... this manner: 0 1 4 1 4 1 4 1 8 1 8 1 2 00 1 2 3 4 3 16 − 3 8 3 8 9 16 1 − 3 7 8 7 6 7 − 12 7 8 7 7 90 0 16 45 2 15 16 45 7 90 . 166 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS Another ... = 6 p! − 2(c 2 + c 4 ) (p − 1)! + c 2 c 4 (p − 2)! , (324a) b A p 4 (C −c 4 I)Ac = 3 p! − c 4 (p − 1)! , (324b) b A p 4 A(C −c 2 I)c = 2 p! − c 2 (p − 1)! , (324c) b...
Ngày tải lên: 13/08/2014, 05:21
Numerical Methods for Ordinary Dierential Equations Episode 7 potx
... − 6 41 − 3 205 − 3 41 3 41 6 41 0 1 − 1777 41 00 00− 341 1 64 449 6 1025 − 289 82 2193 41 00 51 82 33 1 64 12 41 01 41 840 00 0 0 34 105 9 35 9 35 9 280 9 280 41 840 00 000 0 0 34 105 9 35 9 35 9 280 9 280 0 41 840 41 840 − 41 840 000000000− 41 840 41 840 41 840 . The two methods ... 0 61 225 − 2 9 13 900 2 3 200− 53 6 7 04 45 − 107 9 67 90...
Ngày tải lên: 13/08/2014, 05:21
Numerical Methods for Ordinary Dierential Equations Episode 8 ppsx
... illustrated in Figure 3 54( i), for the case of the (1, 3) Pad´e approximation given by R(z)= 1+ 1 4 z 1 − 3 4 z + 1 4 z 2 − 1 24 z 3 . 232 NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS Proof. ... + 1 7 z 2 − 2 105 z 3 + 1 840 z 4 5 1+ 4 9 z + 1 12 z 2 + 1 126 z 3 + 1 30 24 z 4 1 − 5 9 z + 5 36 z 2 − 5 252 z 3 + 5 30 24 z 4 − 1 15120 z 5 6 1+ 5 11 z + 1...
Ngày tải lên: 13/08/2014, 05:21
Numerical Methods for Ordinary Dierential Equations Episode 9 ppsx
... − √ 2 ,T −1 = 1 2 + √ 2 4 1 2 − √ 2 4 √ 2 4 − √ 2 4 . For L-stability, choose λ = ξ −1 2 =1− 1 2 √ 2, and we evaluate A = λT (I −J)T −1 to give the tableau 3 − 2 √ 2 5 4 − 3 4 √ 2 7 4 − 5 4 √ 2 1 1 4 + 1 4 √ 2 3 4 − 1 4 √ 2 1 4 + 1 4 √ 2 3 4 − 1 4 √ 2 . (363g) RUNGE–KUTTA ... α 4 1 − α 5 64 α 1 α 3 + α 1 α 4 + α 2 2 − 3α 2 α 2 1 + α 4 1 − α 6 7...
Ngày tải lên: 13/08/2014, 05:21
Numerical Methods for Ordinary Dierential Equations Episode 10 pot
... b 4 a 42 c 2 + b 4 a 43 c 3 = 1 6 , b 4 a 43 a 32 c 2 = 1 24 , b 2 c 2 2 (1 − c 2 )+b 3 c 2 3 (1 − c 3 )+b 4 c 2 4 (1 − c 4 ) + b 3 a 32 c 2 (2c 3 − c 2 )+b 4 a 42 c 2 (2c 4 − c 2 )+b 4 a 43 c 3 (2c 4 − c 3 )= 1 4 . RUNGE–KUTTA ... c 2 )+b 4 a 42 c 2 (2c 4 − c 2 )+b 4 a 43 c 3 (2c 4 − c 3 )= 1 4 , b 4 a 43 a 32 c 2 = 1 24 . Methods satis...
Ngày tải lên: 13/08/2014, 05:21