Question

Problem # 2: The objective is to solve the following two nonlinear equations using the Newton Raphson algorithm: f(x1 , X2)=-1.5 6(X1-X2)=-0.5 Where: f (x,x2x-1.lx, cos(x,)+11x, sin(x,) f2(X1-X2)-9.9X2-1.1x, sin(%)-iïx, cos(%) 1. Find the Jacobian Matrix 2. Lex0, x 1, use the Newton Raphson algorithm to a find a solution x,x2 such that max{_ 1.5-f(x1, X2 ' |-0.5-f(x1, X2)|}$10

Answer 1

f_1 (x_1, x_2) = -1.5 f_2 (x_1, x_2) = -0.5 where f_1 (x_1, x_2) = x_2^3 - 1.1x_2 Cos (x_1) + 11x_2 Sin (x_1) f_2 (x_1, x_2) = 9.9 x_2^2 - 1.1 x_2 Sin (x) - 11 x_2 Cos (x_1) delta f = J delta x [delta f_1 degrees delta f_2 degrees] = [(partial differential f_1/partial differential x_1) degrees (partial differential f_2/partial differential x_1) degrees (partial differential f_1/partial differential x_2) degrees (partial differential f_2/partial differential x_2) degrees [delta x_1 delta x_2] [x_2^2 - 1.1 x_2 Cos x_1 + 11 x_2 Sin x_1/partial differential x_1 9.9 x_2^2 - 1.1 x_2 Sin x_1 - 11 x_2 Cos x_1/partial differential x_1 x_2^2 - 1.1 x_2 Cos x_1 + 11 x_2 Sin x/partial differential x_2 9.9 x_2^2 - 1.1 x_2 Sin x - 11 x_2 Cos x_1/partial differential x_1] [Sin x_1 - 1.1 x_2 . Cos x_1 - 11 x_2 Sin x_1 -1.1 x_2 Cos x_1 - 11 x_2 Sin x_1 2x_2 - 1.1 Cos x_1 + 11 Sin x_1 19.8 x_2 - 1.1 Sin x_1