1.Answers to the first four subparts
Plotting the two graphs.
The intersection point is (x,y) =(-1.6,1,56) and (1.6,1.56)
2.successive substitution:
3. Newton Raphson:
4.
xsucccesive=1.5;ysuccessive=1.5;
for i= 1:2
xtemp=xsucccesive;
xsucccesive = sqrt(5- ysuccessive.*ysuccessive)
ysuccessive=xtemp.*xtemp -1
end
xnr=1.5;ynr=1.5;
for i= 1:2
xtemp=xnr;
dify1= -ynr/(sqrt(5- ynr.*ynr));
fy1=sqrt(5- ynr.*ynr);
xnr = xnr - (fy1/dify1)
fx2=xtemp.*xtemp -1;
diffx2 = 2*xtemp;
ynr = ynr - (fx2/diffx2)
end
Problem Two: (Based on Chapra, Problems 12.9 Consider the simultaneous nonlinear equations: 2-5-y y+i- 1. Plot...
Q2. Determine the positive roots of the simultaneous nonlinear equations: yx2 y 2 cosx Use a graphical approach to obtain your initial guesses. Plot both the equations in one plot area. You may have two sets of solutions. Considering one of the solutions and selecting initial guesses close to that solution (you can take x = 0.7 and yo = 1.5), use Newton-Raphson Method to solve the system of equations, shown above.e, 0.01 % Q2. Determine the positive roots of...
B. Implement the Newton-Raphson (NR) method for solving nonlinear equations in one dimension. The program should be started from a script M-file. Prompt the user to enter an initial guess for the root. -Use an error tolerance of 107, -Allow at most 1000 iterations. .The code should be fully commented and clear 2. a) Use your NR code to find the positive root of the equation given below using the following points as initial guesses: xo = 4, 0 and-1...
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...
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...
I have a exercise of Numerical Method. help me. Thanks Question 2: Determine the solution of the simultaneous nonlinear equations y-2-3x y+2x 2 Use four iterations of the Newton-Raphson method and employ initial guesses ofx -l; y--1
____________ % This function is a modified versio of the newtmult function obtained % from % “Applied Numerical Methods with MATLAB, Chapra, % 3rd edition, 2012, McGraw-Hill.” function [x,f,ea,iter]=newtmult(func,x0,es,maxit,varargin) % newtmult: Newton-Raphson root zeroes nonlinear systems % [x,f,ea,iter]=newtmult(f,J,x0,es,maxit,p1,p2,...): % uses the Newton-Raphson method to find the roots of % a system of nonlinear equations % input: % f = the passed function % J = the passed jacobian % x0 = initial guess % es = desired percent relative error...
Graphically Determine the solution of the simultaneous nonlinear equations: x² = 5 – y² y+1 = x2
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
Only the matlab nlinear equations x 0.75 Determine the roots of these equations using: a) The Fixed-point iteration method. b) The Newton Raphson method. Employ initial guesses of x y 1.2 and perform the iterations until E.<10%. Note: You can use to solve the problems, but you should sol at least two full iterations manually. AB bl Du Thursd 30/3/ 1. For the displacement in Q3 y 10 e cos at 0 St S 4. a) Plot the displacement y...
matlab help? incorrectQuestion 7 0/0.83 pts Newton-Raphson iteration is to be used to solve the following system of equations: y +1-x3 Calculate the elements of the Jacobian matrix (to 2 decimal places) if the values of x and y in the current iteration are x 1 and y 1.5. Rearrange the equations to formulate the roots problems so that the constants (5 in the first equation and 1 in the second equation) are positive before taking the partial derivatives J.11...