Can you help me to solve equation

based on the Newton-Raphson method and an initial guess x0=(1,1,1)

x2y2 − z2 = 0.3

x cos y − sin 2z = -0.3

x + eyz = −1.1

Answer 1

[Shivam Gothi]

Hello @marwa,

As per my understanding, you are trying to find the solution of set of non-linear equations using Newton-Raphson method.

As the third equation given by you is not clear, I am assuming that the equations you are trying to solve are:

x^2 * y^2 - z^2=0.3;

x cos y − sin 2z = -0.3;

x + y*z = -1.1;

I have attached a code snippet which solves the system of non linear equations containing three variables using Newton Raphson method.

I have used it for the above stated set of equation, and attached the screen-shot of its implementation:

This uses the Function “Newton_Raphson” from below attached file exchange:

https://www.mathworks.com/matlabcentral/fileexchange/71593-newton-raphson-method-for-a-nonlinear-system-of-3-variables

The function returns the solution of three equations in three variables using the Newton-Raphson method. The inputs are symbolic functions, initial guesses and number of iterations.

Refer to the instructions given in the above mentioned file exchange to get a clear understanding of its usage.

I hope it helps !

[marwa]

Thank you for your response, but I want to mention the third equation isn't like you think. I will put the correct equation:

u = x^2*y^2-z^2-0.3;
v = x cos(y)-sin(2*z)+0.3;
w= x=exp^y*z+1.1;

[Shivam Gothi]

hello @marwa,

thankyou for clearifying. In that case, you will get :

[John D'Errico]

@Shivam Gothi

Please do not do homework assignments for students who make no effort. This teaches the student nothing more than that there is someone out there willing to do their homework.

This does not help the forum, since it convinces the student to continue posting their assignments. It convinces other students to do the same, which actively hurts the forum. And it forces me to watch more diligently to close similar future questions from this student.