Dgl-numerisch und analytisch

Heun Start bei A?

A mit Pfeiltasten bewegen

w(x, y) = y^(2) - x
y3: 0.8118
x3: 1.5
m3: w(x3, y3)
n = 1 (slider from -1 to 3, step 1)
h: 2^((-n))
xS: x3 + h
xH: x3 + h / 2
xR: xH
yH: y3 + (m3 * h / 2)
mH: w(xH, yH)
yR: y3 + (mH * h / 2)
mR: w(xR, yR)
yS: y3 + (mR * h)
mS: w(xS, yS)
m: (m3 + (2 * mH) + (2 * mR) + mS) / 6
y4: y3 + (m * h)
x4: x3 + h
A = (0, 0.7)
C1: y(A)
B1: x(A)
B2: B1 + h
B3: B2 + h
B4: B3 + h
B5: B4 + h
AgleichC = true
α = 1 (slider from 0 to 1.5, step 0.1)
b = If(α ≟ 0, 0, 1 / 2 / α)
a = If(α ≟ 0, 1, 1 - b)
Steigungsfeld2 = SlopeField(w(x, y))
A1 = 0 (slider from -5 to 5)
A2 = 1 (slider from -5 to 5)
A3 = 2 (slider from -5 to 5)
A4 = 3 (slider from -5 to 5)
A5 = 4 (slider from -5 to 5)
A6 = 5 (slider from -5 to 5)
A7 = 6 (slider from -5 to 10)
A8 = 7 (slider from -5 to 10)
A9 = 8 (slider from -5 to 10)
A10 = 9 (slider from -5 to 10)
A11 = 10 (slider from -5 to 20)
A12 = 11 (slider from -5 to 20)
A13 = 12 (slider from -5 to 20)
A14 = 13 (slider from -5 to 20)
A15 = 14 (slider from -5 to 20)
A16 = 15 (slider from -5 to 20)
A17 = 16 (slider from -5 to 20)
A18 = 17 (slider from -5 to 20)
A19 = 18 (slider from -5 to 20)
A20 = 19 (slider from -5 to 20)
A21 = 20 (slider from -5 to 20)
A22 = 21 (slider from -5 to 50)
A23 = 22 (slider from -5 to 50)
A24 = 23 (slider from -5 to 50)
A25 = 24 (slider from -5 to 50)
A26 = 25 (slider from -5 to 50)
A27 = 26 (slider from -5 to 50)
A28 = 27 (slider from -5 to 50)
A29 = 28 (slider from -5 to 50)
A30 = 29 (slider from -5 to 50)
A31 = 30 (slider from -5 to 50)
A32 = 31 (slider from -5 to 50)
A33 = 32 (slider from -5 to 50)
B6: B5 + h
B7: B6 + h
B8: B7 + h
B9: B8 + h
B10: B9 + h
B11: B10 + h
B12: B11 + h
B13: B12 + h
B14: B13 + h
B15: B14 + h
B16: B15 + h
A34 = 33
A35 = 34
A36 = 35
A37 = 36
A38 = 37
A39 = 38
A40 = 39
A41 = 40
A42 = 41
A43 = 42
A44 = 43
A45 = 44
A46 = 45
A47 = 46
A48 = 47
A49 = 48
A50 = 49
A51 = 50
A52 = 51
A53 = 52
A54 = 53
A55 = 54
A56 = 55
A57 = 56
A58 = 57
A59 = 58
A60 = 59
A61 = 60
A62 = 61
A63 = 62
A64 = 63
A65 = 64
P3 = NaN
RK: {(0, 0.7), (1 / 2, 0.9045739331100453), (1, 0.9941396540251675), (3 / 2, 0.8117627361267241), (2, 0.08813683542412054), (5 / 2, -0.9028882345250044), (3, -1.4793895856331898), (7 / 2, -1.7469931063656001), (4, -1.9175820543436566), (9 / 2, -2.0559080612874845), (5, -2.1798682510273317), (11 / 2, -2.2951256788717957), (6, -2.403952269383518), (13 / 2, -2.507531326810097), (7, -2.606609025899793), (15 / 2, -2.7017012192457073), (8, -2.7931609880806256)}
H: (xH, yH)
R: (xR, yR)
S: (xS, yS)
Pn: (x3 + h, y3 + (m * h))
yHeun(x, y) = y + ((a * h) * w(x, y)) + ((b * h) * w(x + (α * h), y + ((α * h) * w(x, y))))
C2: yHeun(B1, C1)
C3: yHeun(B2, C2)
C4: yHeun(B3, C3)
C5: yHeun(B4, C4)
C6: yHeun(B5, C5)
C7: yHeun(B6, C6)
C8: yHeun(B7, C7)
C9: yHeun(B8, C8)
C10: yHeun(B9, C9)
C11: yHeun(B10, C10)
C12: yHeun(B11, C11)
C13: yHeun(B12, C12)
C14: yHeun(B13, C13)
C15: yHeun(B14, C14)
C16: yHeun(B15, C15)
yEuler(x, y) = y + (h * w(x, y))
yEuMod(x, y) = y + (h * w(x + (1 / 2 * h), y + ((1 / 2 * h) * w(x, y))))
D1: C1
D2: yEuler(B1, D1)
D3: yEuler(B2, D2)
D4: yEuler(B3, D3)
D5: yEuler(B4, D4)
D6: yEuler(B5, D5)
D7: yEuler(B6, D6)
D8: yEuler(B7, D7)
D9: yEuler(B8, D8)
D10: yEuler(B9, D9)
D11: yEuler(B10, D10)
D12: yEuler(B11, D11)
D13: yEuler(B12, D12)
D14: yEuler(B13, D13)
E1: C1
E2: yEuMod(B1, E1)
E3: yEuMod(B2, E2)
E4: yEuMod(B3, E3)
E5: yEuMod(B4, E4)
E6: yEuMod(B5, E5)
E7: yEuMod(B6, E6)
E8: yEuMod(B7, E7)
E9: yEuMod(B8, E8)
E10: yEuMod(B9, E9)
E11: yEuMod(B10, E10)
E12: yEuMod(B11, E11)
E13: yEuMod(B12, E12)
D15: yEuler(B14, D14)
D16: yEuler(B15, D15)
E14: yEuMod(B13, E13)
E15: yEuMod(B14, E14)
E16: yEuMod(B15, E15)
B: (B1, E1)
D: (B2, E2)
F: (B3, E3)
G: (B4, E4)
I: (B5, E5)
J: (B6, E6)
K: (B7, E7)
L: (B8, E8)
M: (B9, E9)
O: (B10, E10)
P: (B11, E11)
Q: (B12, E12)
T: (B13, E13)
U: (B14, E14)
V: (B15, E15)
W: (B16, E16)
EuMod: {B, D, F, G, I, J, K, L, M, O, P, Q, T, U, V, W}
Z: (B1, E1)
A_1: (B2, E2)
B_1: (B3, E3)
C_1: (B4, E4)
D_1: (B5, E5)
E_1: (B6, E6)
F_1: (B7, E7)
G_1: (B8, E8)
H_1: (B9, E9)
I_1: (B10, E10)
J_1: (B11, E11)
K_1: (B12, E12)
L_1: (B13, E13)
M_1: (B14, E14)
N_1: (B15, E15)
O_1: (B16, E16)
EuModZug = PolyLine({Z, A_1, B_1, C_1, D_1, E_1, F_1, G_1, H_1, I_1, J_1, K_1, L_1, M_1, N_1, O_1})
P_1: (B1, D1)
Q_1: (B2, D2)
R_1: (B3, D3)
S_1: (B4, D4)
T_1: (B5, D5)
U_1: (B6, D6)
V_1: (B7, D7)
W_1: (B8, D8)
Z_1: (B9, D9)
A_2: (B10, D10)
B_2: (B11, D11)
C_2: (B12, D12)
D_2: (B13, D13)
E_2: (B14, D14)
F_2: (B15, D15)
G_2: (B16, D16)
Euler: {P_1, Q_1, R_1, S_1, T_1, U_1, V_1, W_1, Z_1, A_2, B_2, C_2, D_2, E_2, F_2, G_2}
H_2: (B1, D1)
I_2: (B2, D2)
J_2: (B3, D3)
K_2: (B4, D4)
L_2: (B5, D5)
M_2: (B6, D6)
N_2: (B7, D7)
O_2: (B8, D8)
P_2: (B9, D9)
Q_2: (B10, D10)
R_2: (B11, D11)
S_2: (B12, D12)
T_2: (B13, D13)
U_2: (B14, D14)
V_2: (B15, D15)
W_2: (B16, D16)
EulerZug = PolyLine({H_2, I_2, J_2, K_2, L_2, M_2, N_2, O_2, P_2, Q_2, R_2, S_2, T_2, U_2, V_2, W_2})
Z_2: (B1, C1)
A_3: (B2, C2)
B_3: (B3, C3)
C_3: (B4, C4)
D_3: (B5, C5)
E_3: (B6, C6)
F_3: (B7, C7)
G_3: (B8, C8)
H_3: (B9, C9)
I_3: (B10, C10)
J_3: (B11, C11)
K_3: (B12, C12)
L_3: (B13, C13)
M_3: (B14, C14)
N_3: (B15, C15)
O_3: (B16, C16)
Heun: {Z_2, A_3, B_3, C_3, D_3, E_3, F_3, G_3, H_3, I_3, J_3, K_3, L_3, M_3, N_3, O_3}
Q_3: (B1, C1)
R_3: (B2, C2)
S_3: (B3, C3)
T_3: (B4, C4)
U_3: (B5, C5)
V_3: (B6, C6)
W_3: (B7, C7)
Z_3: (B8, C8)
A_4: (B9, C9)
B_4: (B10, C10)
C_4: (B11, C11)
D_4: (B12, C12)
E_4: (B13, C13)
F_4: (B14, C14)
G_4: (B15, C15)
H_4: (B16, C16)
HeunZug = PolyLine({Q_3, R_3, S_3, T_3, U_3, V_3, W_3, Z_3, A_4, B_4, C_4, D_4, E_4, F_4, G_4, H_4})
gl1: x = 3
f = SolveODE(w(x, y), x(A), y(A), 8, 0.05)
C = (-1.1538011906573427, 0.6804063516291949)
E = (-0.4132098345240498, 0.6804063516291949)