Figure CabriII vers. MacOS 1.1.8 Used macro(s): Tangente sur Equation Euler, no name Icon: 0FFFFFFFFFFFFFF0 0FF0000FF0000FF0 0F00000FF00000F0 0F00000FF00000F0 0000000FF0000000 0000000FF0000000 0000000FF0000000 0000000FF0000000 0000000FF0000000 0000000FF0000000 0000000FF0000000 0000000FF0000000 0000000FF0000000 0000000FF0000000 0000000FF0000000 00000FFFFFF00000 Help: "O, I, (x0, y0)" Mth: 0 CN:3, ON:17, FN:1, PO:16 CT: point, CS 0, R, W, t, DS:1 1, GT:1, V, nSt point, CS 0, R, W, t, DS:1 1, GT:1, V, nSt point, CS 0, R, W, t, DS:1 1, GT:1, V, nSt Const: Line, Mth:1, 0, 0, CN:2, VN:2, Const: 1 2 Perp, Mth:0, 0, 0, CN:2, VN:2, Const: 1 4 Perp, Mth:0, 0, 0, CN:2, VN:2, Const: 3 4 Perp, Mth:0, 0, 0, CN:2, VN:2, Const: 3 5 Int, Mth:0, 0, 0, CN:2, VN:1, Const: 4 6 Int, Mth:0, 0, 0, CN:2, VN:1, Const: 5 7 Cir, Mth:1, 0, 0, CN:2, VN:2, Const: 1 2 Int, Mth:1, 0, 256, CN:2, VN:1, Const: 5 10 Seg, Mth:0, 0, 0, CN:2, VN:2, Const: 8 11 Par, Mth:0, 0, 0, CN:2, VN:2, Const: 2 12 Int, Mth:0, 0, 0, CN:2, VN:1, Const: 5 13 Vec, Mth:0, 0, 0, CN:2, VN:2, Const: 9 1 Tran, Mth:0, 0, 0, CN:2, VN:1, Const: 14 15 Vec, Mth:0, 0, 0, CN:2, VN:2, Const: 1 2 Tran, Mth:0, 0, 0, CN:2, VN:1, Const: 16 17 Seg, Mth:0, 0, 0, CN:2, VN:2, Const: 1 18 Par, Mth:0, 1, 0, CN:2, VN:2, Const: 3 19, Br, W, t, DS:1 1, GT:0, V, nSt Figure description: Window center x: 5.8 y: -1.73_ 1: Pt, 0, CN:0, VN:1 R, W, t, DS:1 1, GT:1, I, nSt Val: 0 0 2: Axes, 1, CN:1, VN:3 dGr, W, t, DS:1 1, GT:0, I, nSt Const: 1, Val: 1 0, 0 1 "O", NP: -91, 76, NS: 14, 12 3: Pt, 0, CN:0, VN:1 R, W, t, DS:1 1, GT:1, V, nSt Val: -2.7 -2.4 p: 0, Times, S: 12 C: 6 Fa: 0 4: Line, 0, CN:1, VN:2 G, W, t, DS:1 1, GT:0, I, nSt Const: 3, Val: 1 0 "I", NP: -10, 79, NS: 10, 12 5: Pt/, 0, CN:1, VN:3 R, W, t, DS:1 1, GT:1, V, nSt Const: 4, Val: -0.43_ -2.4 p: 0, Times, S: 12 C: 6 Fa: 0 6: Line, 0, CN:2, VN:2 lGr, W, t, DS:1 1, GT:0, I, nSt Const: 3 5 7: Pt/, 0, CN:1, VN:3 R, W, t, DS:1 1, GT:1, I, nSt Const: 6, Val: -7.56_ -2.4 8: Pt/, 0, CN:1, VN:3 R, W, t, DS:1 1, GT:1, I, nSt Const: 6, Val: 5.23_ -2.4 9: Seg, 0, CN:2, VN:2 G, W, t, DS:1 1, GT:0, I, nSt Const: 7 8 "x1", NP: 90, 81, NS: 17, 17 10: Pt/, 0, CN:1, VN:3 R, W, t, DS:1 1, GT:1, V, nSt Const: 9, Val: 2.93_ -2.4 p: 0, Times, S: 12 C: 5 Fa: 0, p: 1, Times, S: 10 C: 5 Fa: 512 11: Perp, 0, CN:2, VN:2 lGr, W, t, DS:1 1, GT:0, V, nSt Const: 3 6 "(x0, y0)", NP: 23, -51, NS: 43, 17 12: Pt, 0, CN:0, VN:1 R, W, t, DS:1 1, GT:1, V, nSt Val: 0.56_ 1.16_ p: 0, Times, S: 12 C: 3 Fa: 0, p: 2, Times, S: 10 C: 3 Fa: 512, p: 3, Times, S: 12 C: 3 Fa: 0, p: 6, Times, S: 10 C: 3 Fa: 512, p: 7, Times, S: 12 C: 3 Fa: 0 13: Perp, 0, CN:2, VN:2 O, W, t, DS:1 1, GT:0, V, nSt Const: 12 6 14: Perp, 0, CN:2, VN:2 O, W, t, DS:1 1, GT:0, I, nSt Const: 12 11 "x0", NP: 18, 72, NS: 17, 17 15: Int, 0, CN:2, VN:1 R, W, t, DS:1 1, GT:1, V, nSt Const: 6 13 p: 0, Times, S: 12 C: 2 Fa: 0, p: 1, Times, S: 10 C: 2 Fa: 512 "y0", NP: -95, -50, NS: 17, 17 16: Int, 0, CN:2, VN:1 R, W, t, DS:1 1, GT:1, V, nSt Const: 11 14 p: 0, Times, S: 12 C: 2 Fa: 0, p: 1, Times, S: 10 C: 2 Fa: 512 17: Cir, 0, CN:2, VN:2 lGr, W, t, DS:5 8, GT:0, V, nSt Const: 3 5 "J", NP: -78, -9, NS: 11, 12 18: Int, 256, CN:2, VN:1 R, W, t, DS:1 1, GT:1, V, nSt Const: 11 17 p: 0, Times, S: 12 C: 6 Fa: 0 19: Seg, 0, CN:2, VN:2 G, W, t, DS:1 1, GT:0, V, nSt Const: 15 18 20: Par, 0, CN:2, VN:2 G, W, t, DS:1 1, GT:0, V, nSt Const: 5 19 "1/x0", NP: -107, 21, NS: 26, 17 21: Int, 0, CN:2, VN:1 R, W, t, DS:1 1, GT:1, V, nSt Const: 11 20 p: 0, Times, S: 12 C: 9 Fa: 0, p: 3, Times, S: 10 C: 9 Fa: 512 22: Vec, 0, CN:2, VN:2 V, W, t, DS:1 1, GT:0, I, nSt Const: 16 3 "1/x0 - y0", NP: -105, 117, NS: 47, 17 23: Tran, 0, CN:2, VN:1 R, W, t, DS:1 1, GT:1, V, nSt Const: 21 22 p: 0, Times, S: 12 C: 5 Fa: 0, p: 3, Times, S: 10 C: 5 Fa: 512, p: 4, Times, S: 12 C: 5 Fa: 0, p: 8, Times, S: 10 C: 5 Fa: 512 24: Vec, 0, CN:2, VN:2 V, W, t, DS:1 1, GT:0, V, nSt Const: 3 5 "Pente y'0 de la mthode d'Euler", NP: -41, 140, NS: 84, 29 25: Tran, 0, CN:2, VN:1 P, W, t, DS:1 1, GT:0, V, nSt Const: 23 24 p: 0, Times, S: 12 C: 4 Fa: 0, p: 8, Times, S: 10 C: 4 Fa: 512, p: 9, Times, S: 12 C: 4 Fa: 0 26: Seg, 0, CN:2, VN:2 G, W, t, DS:1 1, GT:0, I, nSt Const: 3 25 27: Par, 0, CN:2, VN:2 Br, W, t, DS:1 1, GT:0, I, nSt Const: 12 26 28: Perp, 0, CN:2, VN:2 lBl, W, t, DS:1 1, GT:0, V, nSt Const: 10 6 "(x1, y'1) dans la mthode d'Euler", NP: 59, 34, NS: 84, 29 29: Int, 0, CN:2, VN:1 R, W, t, DS:1 1, GT:1, V, nSt Const: 27 28 p: 0, Times, S: 12 C: 9 Fa: 0, p: 2, Times, S: 10 C: 9 Fa: 512, p: 3, Times, S: 12 C: 9 Fa: 0, p: 7, Times, S: 10 C: 9 Fa: 512, p: 8, Times, S: 12 C: 9 Fa: 0 30: Text, 0, CN:0, VN:1 B, W, BTh:1, DS:1 1, GT:0, V, nSt Val: -9 -165 0, A, nP, TP: -0.3, 5.5, TS: 12.9, -1 " Itration sur l'quation d'Euler y' + y = 1/x Mthode des trapzes (moyenne des pentes des tangentes)" p: 0, Times, S: 14 C: 5 Fa: 1 31: Seg, 0, CN:2, VN:2 P, W, t, DS:1 1, GT:0, V, nSt Const: 12 29 Ma: Tangente sur Equation Euler, Const: 3 i: 0 5 i: 0 29 i: 0 48: Ma R, F No1, VN:2 Br, W, t, DS:1 1, GT:0, I, nSt "x2 = x1 + (x1 - x0)", NP: 136, 78, NS: 94, 17 49: Refl, 0, CN:2, VN:1 R, W, t, DS:1 1, GT:1, V, nSt Const: 15 28 p: 0, Times, S: 12 C: 9 Fa: 0, p: 1, Times, S: 10 C: 9 Fa: 512, p: 2, Times, S: 12 C: 9 Fa: 0, p: 6, Times, S: 10 C: 9 Fa: 512, p: 7, Times, S: 12 C: 9 Fa: 0, p: 12, Times, S: 10 C: 9 Fa: 512, p: 13, Times, S: 12 C: 9 Fa: 0, p: 17, Times, S: 10 C: 9 Fa: 512, p: 18, Times, S: 12 C: 9 Fa: 0 50: Perp, 0, CN:2, VN:2 lBl, W, t, DS:1 1, GT:0, V, nSt Const: 49 6 "(x2, y'2) dans la mthode d'Euler", NP: 163, 33, NS: 84, 29 51: Int, 0, CN:2, VN:1 R, W, t, DS:1 1, GT:1, V, nSt Const: 48 50 p: 0, Times, S: 12 C: 9 Fa: 0, p: 2, Times, S: 10 C: 9 Fa: 512, p: 3, Times, S: 12 C: 9 Fa: 0, p: 7, Times, S: 10 C: 9 Fa: 512, p: 8, Times, S: 12 C: 9 Fa: 0 "y1 par la mthode des trapzes", NP: 93, -9, NS: 92, 29 52: Mid, 0, CN:2, VN:1 V, W, t, DS:1 1, GT:1, V, nSt Const: 12 51 p: 0, Times, S: 12 C: 5 Fa: 0, p: 1, Times, S: 10 C: 5 Fa: 512, p: 2, Times, S: 12 C: 5 Fa: 0 53: Vec, 0, CN:2, VN:2 P, W, t, DS:1 1, GT:0, V, nSt Const: 3 25 54: Seg, 0, CN:2, VN:2 lGr, W, t, DS:1 1, GT:0, V, nSt Const: 25 5 55: Seg, 0, CN:2, VN:2 lGr, W, t, DS:1 1, GT:0, V, nSt Const: 25 23 56: Seg, 0, CN:2, VN:2 V, W, t, DS:1 1, GT:0, V, nSt Const: 12 51 57: Seg, 0, CN:2, VN:2 P, W, t, DS:1 1, GT:0, V, nSt Const: 29 51 58: Text, 0, CN:0, VN:1 B, W, BTh:1, DS:1 1, GT:0, V, nSt Val: 262 -82 0, A, nP, TP: 8.73_, 2.73_, TS: 6.46_, -8.93_ "Dans cette mthode de Runge, pour valuer l'ordonne y1 d'un point d'abscisse x1, partir d'une condition initiale (x0, y0), on applique la mthode d'Euler une premire fois - ce qui donne le point (x1, y'1), puis on l'applique nouveau avec le mme pas, et la condition initiale (x1, y'1), ce qui donne le point (x2, y'2). On choisit alors pour pente la moynne des pentes, c'est--dire qu'en pratique y1 est le milieu du segment d'extrmits (x0, y0) et (x2, y'2). Runge a remarqu le premier que cette mthode donnait une approximation d'ordre 2." p: 0, Times, S: 12 C: 11 Fa: 0, p: 53, Times, S: 12 C: 5 Fa: 0, p: 54, Times, S: 10 C: 5 Fa: 512, p: 55, Times, S: 12 C: 11 Fa: 0, p: 78, Times, S: 12 C: 5 Fa: 0, p: 79, Times, S: 10 C: 5 Fa: 512, p: 80, Times, S: 12 C: 11 Fa: 0, p: 115, Times, S: 12 C: 3 Fa: 0, p: 118, Times, S: 10 C: 3 Fa: 512, p: 119, Times, S: 12 C: 3 Fa: 0, p: 122, Times, S: 10 C: 3 Fa: 512, p: 123, Times, S: 12 C: 3 Fa: 0, p: 124, Times, S: 12 C: 11 Fa: 0, p: 199, Times, S: 12 C: 9 Fa: 0, p: 202, Times, S: 10 C: 9 Fa: 512, p: 203, Times, S: 12 C: 9 Fa: 0, p: 207, Times, S: 10 C: 9 Fa: 512, p: 208, Times, S: 12 C: 9 Fa: 0, p: 209, Times, S: 12 C: 11 Fa: 0, p: 282, Times, S: 12 C: 9 Fa: 0, p: 285, Times, S: 10 C: 9 Fa: 512, p: 286, Times, S: 12 C: 9 Fa: 0, p: 290, Times, S: 10 C: 9 Fa: 512, p: 291, Times, S: 12 C: 9 Fa: 0, p: 292, Times, S: 12 C: 11 Fa: 0, p: 315, Times, S: 12 C: 9 Fa: 0, p: 318, Times, S: 10 C: 9 Fa: 512, p: 319, Times, S: 12 C: 9 Fa: 0, p: 323, Times, S: 10 C: 9 Fa: 512, p: 324, Times, S: 12 C: 9 Fa: 0, p: 325, Times, S: 12 C: 11 Fa: 0, p: 407, Times, S: 12 C: 5 Fa: 0, p: 408, Times, S: 10 C: 5 Fa: 512, p: 409, Times, S: 12 C: 11 Fa: 0, p: 448, Times, S: 12 C: 3 Fa: 0, p: 450, Times, S: 10 C: 3 Fa: 512, p: 451, Times, S: 12 C: 3 Fa: 0, p: 454, Times, S: 10 C: 3 Fa: 512, p: 455, Times, S: 12 C: 3 Fa: 0, p: 456, Times, S: 12 C: 11 Fa: 0, p: 459, Times, S: 12 C: 9 Fa: 0, p: 462, Times, S: 10 C: 9 Fa: 512, p: 463, Times, S: 12 C: 9 Fa: 0, p: 467, Times, S: 10 C: 9 Fa: 512, p: 468, Times, S: 12 C: 9 Fa: 0, p: 469, Times, S: 12 C: 11 Fa: 0, p: 472, Times, S: 12 C: 4 Fa: 0 59: Pt/, 0, CN:1, VN:3 R, W, t, DS:1 1, GT:1, I, nSt Const: 27, Val: -1.63_ 3.10190076030412 60: Pt/, 0, CN:1, VN:3 R, W, t, DS:1 1, GT:1, I, nSt Const: 27, Val: 6.66_ -4.19920968387355 61: Pt/, 0, CN:1, VN:3 R, W, t, DS:1 1, GT:1, I, nSt Const: 48, Val: 8.03_ -2.20395890604763 62: Pt/, 0, CN:1, VN:3 R, W, t, DS:1 1, GT:1, I, nSt Const: 48, Val: -0.4 -0.0728343478010754 63: Seg, 0, CN:2, VN:2 Br, W, t, DS:1 1, GT:0, V, nSt Const: 59 12 64: Seg, 0, CN:2, VN:2 Br, W, t, DS:1 1, GT:0, V, nSt Const: 51 61 65: Seg, 0, CN:2, VN:2 Br, W, t, DS:1 1, GT:0, V, nSt Const: 29 60 66: Seg, 0, CN:2, VN:2 Br, W, t, DS:1 1, GT:0, V, nSt Const: 29 62 67: Pt/, 0, CN:1, VN:3 R, W, t, DS:1 1, GT:1, I, nSt Const: 14, Val: -4.3 1.16_ 68: Pt/, 0, CN:1, VN:3 R, W, t, DS:1 1, GT:1, I, nSt Const: 14, Val: 6.33_ 1.16_ 69: Seg, 0, CN:2, VN:2 O, W, t, DS:1 1, GT:0, V, nSt Const: 67 68 70: Pt/, 0, CN:1, VN:3 R, W, t, DS:1 1, GT:1, I, nSt Const: 6, Val: -5.43_ -2.4 71: Pt/, 0, CN:1, VN:3 R, W, t, DS:1 1, GT:1, I, nSt Const: 6, Val: 7.2 -2.4 72: Seg, 0, CN:2, VN:2 lGr, W, t, DS:1 1, GT:0, V, nSt Const: 70 71