Use the continuation method and the Runge-Kutta method of order four with N = 1 on the following nonlinear systems using x(0) = 0. Are the answers here comparable to Newton's method or are they suitable initial approximations for Newton's method?
a. x1 (1 − x1) + 4x2 = 12,
(x1 − 2)2 + (2x2 − 3)2 = 25.
Compare to 10.2(5c).
b. 5x21 − x22= 0,
x2 − 0.25(sin x1 + cos x2) = 0.
Compare to 10.2(5d).
c. 15x1 + x22 − 4x3 = 13,
x21 + 10x2 − x3 = 11.
x32 − 25x3 = − 22
Compare to 10.2(6c).
d. 10x1 − 2x22+ x2 − 2x3 − 5 = 0,
8x22+ 4x23 − 9 = 0.
8x2 x3 + 4 = 0
Compare to 10.2(6d).