MATLAB CODE;
clc;
clear all;
close all;
function [ xz fs k ]=Newton1(x0)
format long
tol=5*eps;
c(1)=x0;
syms x;
f=exp(-0.5*x)*cos(5*x)-0.5 ;
for k=1:1000
l1=subs(f,c(k));
l2=subs(diff(f),c(k));
c(k+1)=c(k)-l1/l2;
l3=(subs(f,c(k+1)));
fs=l3;
xz=c(k+1);
if (abs(l3) < tol)
break;
end
end
end
%%%%%%% TEST %%%% %%%
[x fs k]=Newton1(0);
fprintf(' x= %f \n',x);
fprintf(' fx= %1.32f \n',fs);
fprintf(' k= %f \n',k);
if k>1000
fprintf('Iteration diverged');
end
MATLAB O/P::
x= 1.164097
fx= -0.00000000000000006861264023336157
k= 7.000000
>>
%%%%%%%%TEST%%%%%%
clc;
close all;
clear all;
format long;
[x fs k]=Newton1(1.5);
fprintf(' x= %f \n',x);
fprintf(' fx= %1.32f \n',fs);
fprintf(' k= %f \n',k);
if k>1000
fprintf('Iteration diverged');
end
MATLAB O/P:
x= 1.311127
fx= -0.00000000000000002916434802119459
k= 6.000000
%%%%%%%%%%%%%TEST%%%%%
clc;
close all;
clear all;
format long;
[x fs k]=Newton1(2);
fprintf(' x= %f \n',x);
fprintf(' fx= %1.32f \n',fs);
fprintf(' k= %f \n',k);
if k>1000
fprintf('Iteration diverged');
end
MATLAB O/P:
x= 2.399596
fx= -0.24611144691801684070142641758139
k= 1000.000000
>>>>>>>>>>>>>Iteration
diverged
Let the mathematical function f(x) be defined as: f(x) = exp(-0.5x) cos(5x)-0.5 , x 〉 0 Write a ...
Please follow the instructions without using other solutions. Thank you in advance Let the mathematical function flu) be defined as: f(x)-exp-0.5x)cos(5x) - 0.5 .x>0 Write a Matlab function called Newton1 that would find the zero based on a passing initial guess as an input argument x0. The function returns the estimated zero location x, the function value at the zero location (f) and the number of iteration k. The iteration function converges if f(%) < 5"eps and it should diverge...
The function should starts as: function [x,fs,k]=Newton1(x0) % enter your code here end >> [x,f,k]=Newton1(0) x = 1.1641, f = -1.6653e-16, k = 7 >> [x,f,k]=Newton1(0.1) x = 0.1972, f = 1.1102e-16, k = 5 >> [x,f,k]=Newton1(1.5) x = 1.3111, f = -1.1102e-16, k = 6 >> [x,f,k]=Newton1(2) Warning iteration diverged, x = 2.8808, f = -0.5624, k = 1000 Let the mathematical function f(x) be defined as: f(x) = exp(-0.5x) cos(5x)-0.5 , x 〉 0...
in matlab -Consider the equation f(x) = x-2-sin x = 0 on the interval x E [0.1,4 π] Use a plot to approximately locate the roots of f. To which roots do the fol- owing initial guesses converge when using Function 4.3.1? Is the root obtained the one that is closest to that guess? )xo = 1.5, (b) x0 = 2, (c) x.-3.2, (d) xo = 4, (e) xo = 5, (f) xo = 27. Function 4.3.1 (newton) Newton's method...
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...
Please answer all questions Q2 2015 a) show that the function f(x) = pi/2-x-sin(x) has at least one root x* in the interval [0,pi/2] b)in a fixed-point formulation of the root-finding problem, the equation f(x) = 0 is rewritten in the equivalent form x = g(x). thus the root x* satisfies the equation x* = g(x*), and then the numerical iteration scheme takes the form x(n+1) = g(x(n)) prove that the iterations converge to the root, provided that the starting...
5.1.2 Open Methods - Newton-Raphson Method Xi+1= xi – FOTO Matlab Code Example:4 function mynewtraph (f, f1,x0,n) Xx0; for ilin x = x - f(x)/f1(x); disp (li if f(x) <0.01 f(x))) break end end end Matlab Code from Chapra function [root, ea, iter)=newtraph (func,dfunc, xr, es,maxit,varargin) newtraph: Newton-Raphson root location zeroes 8 [root, ea, iter)-newtraph (func, dfunc, xr, es,maxit,pl,p2, ...): $uses Newton-Raphson method to find the root of fune input: func- name of function 8dfunc = name of derivative of...
45-3. Modify the code used in Example 4 to find the root only at f(x)<0.01 using Newton-Rephson Method without showing any iteration. Also find the root of equation, f(x) = x 9-3x -10, take initial guess, Xo=2 العقدة College of 9:05 mybb.qu.edu.ca Numerical Methods (Lab.) GENG 300 Summer 2020 5.1.2 Open Methods - Newton-Raphson Method f(x) *1+1 = x; - Matlab Code Example:4 function mynewtraph.t1.x0,-) XXO for ilin x - x - x)/1 x) disp 1 x) <0.01 break end...
3.Consider the following function where a is a positive constant exp(x / a) x<0 f(x) exp(-x/a) r >0 (a) Compute the area bounded by f(x) and the x-axis. Graph f(x) against x for a 2 and a 0.5. (b) Find the Fourier transform F(o) of f(x) (c) Graph F(o) against ω for the same two values of a mentioned (d)Explain what happens to f(x) and F(o) when a tends to zero. F(o) f(x)exp(-icox)dx 3.Consider the following function where a is...