Solve two non linear equations using Newton Raphson method x(1)^2 - 2x(1) - x(2) - 3 = 0 and x(1)^2 + x(2)^2 - 41 = 0

f(1) = x(1)^2 - 2x(1) - x(2) - 3 and. f(2) = x(1)^2 + x(2)^2 - 41 Where x(1) and x(2) are unknowns . For the first iteration put x(1) = 2 and x(2) = 3 . Solve using NR method these two non linear equations.

[Steven Lord]

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Answer 1

[Walter Roberson]

syms x [1 2]
f(1,1) = x(1)^2 - 2*x(1) - x(2) - 3;
f(2,1) = x(1)^2 + x(2)^2 - 41

f = 

sol = vpasolve(f, [x(1), x(2)], [2;3])

sol = struct with fields:
    x1: [4x1 sym]
    x2: [4x1 sym]

subs(f.', sol)

ans = 

sol.x1

ans = 

sol.x2

ans = 

●

sol2 = solve(f, 'maxdegree', 3)

sol2 = struct with fields:
    x1: [4x1 sym]
    x2: [4x1 sym]

simplify(expand(sol2.x1))

ans = 

simplify(expand(sol2.x2))

ans =