ZuoTi.Pro
Question

Q5) consider the nonlinear system x3 - 3xy2 - 2x +2 = 0 3x2y - y3 - 2y = 0 Find x and y by Newton-Raphson method if x =1, x2
engineering   Chemical-Engineering   
0 0
Add a comment Improve this question Transcribed image text
Next > < Previous
Sort answers by oldest

Homework Answers

Answer #1

A system of non - linear equations takes a lot of time to solve by hand but can be solved easily by using MATLAB

I explained the solution detailedly by hand and also provided the MATLAB code for your understanding

This is a lengthy answer. I'm hoping that you have some idea about MATLAB. If you don't, don't worry. I explained everything in detail.

Please give a thumbs up if you like my answer. Leave a comment if you have any doubt. Good Luck!

equations is Griven system of non-linear x - 3xy - 2x + 2 = 0 3x²y -ye - 24 [2] [:] Newton - Raphson method for system of eqJE 3x² By²-2 - 6xy 3 x ² 34 22 6xy Iteration 1 - JO) = J at x i. e Jat x, y ho have xM+) _ £12 [Jen] If (200)] n=0 = x ² 2 2sterations, - (2) (1) x x [JC10] [f (x ) -0.394 C-l-oy -3.78 - 0.88 37 0.6003 steration 3 : (3) x x (2) - [5 (27] [ f cx (2)]In the above images, inverse of J is calculated in MATLAB. Type inv(J) to get inverse matrix

MATLAB CODE

Editor Window: Type the below code in editor window. Save this code as "NR.m" file for the code to work

function [f,J,inverseJ,x0,xnew]= NR(x,y)
x0=[x;y];
f1 = x^3 - 3*x*y^2 - 2*x + 2;
f2 = 3*x^2*y - y^3 - 2*y;
f=[f1;f2];
J = [3*x^2 - 3*y^2 - 2 -6*x*y; 6*x*y 3*x^2 - 3*y^2 - 2];
inverseJ = inv(J);
xnew = x0 - inverseJ*f;

Iteration 1

Type this in command window and click enter

[f,J,inverseJ,x0,xnew]= NR(1,1)

Output

This will be the output displayed:

f =
-2
0
J =
-2 -6
6 -2
inverseJ =
-0.0500 0.1500
-0.1500 -0.0500
x0 =
1
1
xnew =
0.9000
0.7000

Now again call your function by entering these xnew values as shown below

Iteration 2

Type this in command window

[f,J,inverseJ,x0,xnew]= NR(0.9,0.7)

Output

This will be the output displayed:

f =
-0.3940
-0.0420
J =
-1.0400 -3.7800
3.7800 -1.0400
inverseJ =
-0.0677 0.2459
-0.2459 -0.0677
x0 =
0.9000
0.7000
xnew =
0.8837
0.6003

Similarly, if you repeat the above process for another 3 times, after 5th iteration the values will be converged and required x,y values are obtained as shown below:

>> [f,J, inverseJ, x0, xnew]= NR (0.8846,0.5897) f = 1.0e-03 * 0.1661 -0.1148 = -3.1299 -0.6957 -0.6957 3.1299 inverseJ -0.06

Therefore, the required values are (x, y)= (0.8846, 0.5897)

0 0
Add a comment
Know the answer?
Add Answer to:
Q5) consider the nonlinear system x3 - 3xy2 - 2x +2 = 0 3x2y - y3...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions

  • Assignment 2 Q.1 Find the numerical solution of system of differential equation y" =t+2y + y',...

    Assignment 2 Q.1 Find the numerical solution of system of differential equation y" =t+2y + y', y(0)=0, at x = 0.2 and step length h=0.2 by Modified Euler method y'0)=1 Q.2. Write the formula of the PDE Uxx + 3y = x + 4 by finite difference Method . Q.3. Solve the initial value problem by Runga - Kutta method (order 4): y" + y' – 6y = sinx ; y(0) = 1 ; y'(0) = 0 at x =...

  • 3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1...

    3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1 < x2 < X3. Suppose that y = ax + by + c is a parabola passing through the three points (x1, yı), (x2, y), and (x3, Y3). We have that a, b, and c must satisfy i = ax + bx + C V2 = ax + bx2 + c y3 = ax} + bx3 + c Let D = x X2 1....

  • Problem # 2: The objective is to solve the following two nonlinear equations using the Newton...

    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

  • 3. A nonlinear system: In class we learned how to use Taylor expansion up to the 1* order term to...

    3. A nonlinear system: In class we learned how to use Taylor expansion up to the 1* order term to solve a system of two non-linear equations; u(x.y)- 0 and v(x.y)-0. This method is also called Newton-Raphson method. (a) As we did in lecture, expand u and v in Taylor series up to the 1st order and obtain the iterative formulas of the method. (In the exam you should have this ready in your formula sheet). 1.2) as an initial...

  • 2. Consider the nonlinear BVP y" = 2y3 – 6y – 2x", 15152, y(1) = 2,...

    2. Consider the nonlinear BVP y" = 2y3 – 6y – 2x", 15152, y(1) = 2, y(2) Use h = 0.1 to approximate the solution using the nonlinear shooting method. Compare the approximate solution with the exact solution: y(x) = x+

  • Assuming our input training data is: (Xi- 2, Y0). (X2-5, Y2-1). (X3-3. Y3-0), (X3-10. Y3-1). let ...

    Logic Regression Assuming our input training data is: (Xi- 2, Y0). (X2-5, Y2-1). (X3-3. Y3-0), (X3-10. Y3-1). let us use the logistic regression to classify the data. o a) Please write down the overall loss function for the logistic regression o b) please write down the gradient for the corresponding loss function at (x = 0). Assuming our input training data is: (Xi- 2, Y0). (X2-5, Y2-1). (X3-3. Y3-0), (X3-10. Y3-1). let us use the logistic regression to classify the...

  • Consider the solution of the nonlinear system of equations f1(x,y)=2x-4cos(y)=0 f2(x,y)=4xsin(y)=0 We want to start with...

    Consider the solution of the nonlinear system of equations f1(x,y)=2x-4cos(y)=0 f2(x,y)=4xsin(y)=0 We want to start with (x0,90)=(0,7/6) and apply Newton's method to compute (X7,71). Whic one of the following(s) is/are true: (1) The solutions are (0, 1/2) and (-2, 1) 2 (II) The Jacobian evaluated at (0,1/2) is (II) (X1,81) = (0,5 +13) Select one: O a. (I) and (11) b. (II) and (111) c. (l) and (III) O d. None of these O e.(I), (II) and (III)

  • 4) (16 points) The function f(x)= x? – 2x² - 4x+8 has a double root at...

    4) (16 points) The function f(x)= x? – 2x² - 4x+8 has a double root at x = 2. Use a) the standard Newton-Raphson, b) the modified Newton-Raphson to solve for the root at x = 2. Compare the rate of convergence using an initial guess of Xo = 1,2. 5) (14 points) Determine the roots of the following simultaneous nonlinear equations using a) fixed-point iteration and b) the Newton-Raphson method: y=-x? +x+0,75 y + 5xy = r? Employ initial...

  • 2. Use implicit differentiation to find y' a. x – 2x²y + 3xy2 = 38

    2. Use implicit differentiation to find y' a. x – 2x²y + 3xy2 = 38

  • 20: Solve the system of equations using substitution method. 2x+5y=26 X+ y= 10 21: Solve the...

    20: Solve the system of equations using substitution method. 2x+5y=26 X+ y= 10 21: Solve the following equation. x-x1/2-6= 0 22: Solve the following system of equations, using elimination method. 2x+3y = 5 5x- y = 4 23: Solve the system of nonlinear equations. Any Method. Y?=x2-9 2y= x-3 24: Convert the log into exponent form. Ln (3x-5)2= 16 25: f(x)= 1/x in words explain the transformation of the following functions. a. g(x) = 1/ (x-3) +5 b. h(x)= -1/(x+2)...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT