Page 214 - Applied Numerical Methods Using MATLAB

PROBLEMS 203
4.7 Newton Method for Systems of Nonlinear Equations
Apply the routine “newtons()” (Section 4.6) and the MATLAB built-in
routine “fsolve()” (with [x0 y0] = [1 0.5]) to solve the following systems
of equations. Fill in Table P4.7 with the results.
2
2
(a) x + y = 1 (P4.7.1)
2
x − y = 0
(b) 5cosθ 1 + 6cos(θ 1 + θ 2 ) = 10
(P4.7.2)
5sinθ 1 + 6sin(θ 1 + θ 2 ) = 4
2
2
(c) 3x + 4y = 3
√ (P4.7.3)
2 2
x + y = 3/2
3
(d) x + 10x 1 − x 2 = 5
1 (P4.7.4)
3
x 1 + x − 10x 2 =−1
2
√
2 2
(e) x − 3xy + 2y = 10
√ (P4.7.5)
2
4x + 3 3xy + y = 22
3
3
(f) x y − y − 2x =−16
(P4.7.6)
2
x − y =−1
2
2
(g) x + 4y = 16 (P4.7.7)
2
xy = 4
5
y
(h) xe − x + y = 3
(P4.7.8)
x + y + tan x − sin y = 0
(i) 2log y − x = 0
(P4.7.9)
xy − y = 1
(j) 12xy − 6x =−1
(P4.7.10)
2
2
60x − 180x y − 30xy = 1
4.8 Newton Method for Systems of Nonlinear Equations
Apply the routine “newtons()” (Section 4.6) and the MATLAB built-in
routine “fsolve()” (with [x0y0z0] = [1 1 1]) to solve the following
systems of equations. Fill in Table P4.8 with the results.
(a) xyz =−1
2
2
2
x + 2y + 4z = 7 (P4.8.1)
3
2
2x + y + 6z = 7
(b) xyz = 1
2
3
2
x + 2y + z = 4 (P4.8.2)
2
3
x + 2y − z = 2
2
2
2
(c) x + 4y + 9z = 34
2
2
x + 9y − 5z = 40 (P4.8.3)
2
x z − y = 7
2
2
(d) x + 2sin(yπ/2) + z = 0
−2xy + z = 3 (P4.8.4)
2
e x+y − z = 0