Using Newton method for solving nonlinear system

2023 11 15
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更新时间：2023 11 15
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Hi guys, please help me write a code program for my homework.
This is my lesson:
We have a lake and we want to determine its maximum teamperature, the temperature is T, and other affecting factors are the temperature of surrounding environment(Te), the amounts of UV rays(UV), the amounts of nutrients(N).
F1(T,Te,UV,N)=T−(Te​+0.5*UV−0.2*N)
F2(T,Te,UV,N)=Te-20
F3(T,Te,UV,N)=UV-5
F4(T,Te,UV,N)=N-2
T_zero=25, Te_zero=20, UV_zero=4, N_zero=1
Thanks to all. Please help me because i have tried lots of times but it just show a wrong result. And i don't have enough knowledge for solving this.

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Khai
Khai 2023-11-15
function main()
% Chọn điểm bắt đầu trong D
X0 = [25; 20; 4; 1];
% Áp dụng phương pháp Newton
X = newtons_method(X0);
% Hiển thị kết quả
disp('Kết quả:')
disp(['Nhiệt độ nước lớn nhất là: ', num2str(X(1))]);
end
function F = equations(X)
% Hệ phương trình phi tuyến
F = [X(1) - (X(2) + 0.5 * X(3) - 0.2 * X(4));
X(2) - 20;
X(3) - 5;
X(4) - 2];
end
function J = jacobian(X)
% Ma trận Jacobi
J = [1, -0.5, -0.1, 0.2;
0, 1, 0, 0;
0, 0, 1, 0;
0, 0, 0, 1];
end
function X = newtons_method(X0)
% Phương pháp Newton
max_iterations = 100;
tolerance = 1e-6;
X = X0;
for i = 1:max_iterations
F = equations(X);
J = jacobian(X);
delta_X = -J \ F;
X = X + delta_X;
if norm(delta_X, inf) < tolerance
break;
end
end
end
Khai
Khai 2023-11-15
can someone help me to fix my code programe please

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Khai
Khai
2023-11-15

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Khai
Khai
2023-11-15

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