Question

Homework 4 - False Position Find the zeros of the function f(x) within the interval (-4, 6) using the False Position method with f(-4) > 0 what you must know before you start working on the homework: f(-1) <0 f(x) = sin(21(x/5) + exp(x/5) f(+6) > 0 (a) Write a Matlab function that computes the values for f(x) when xis given as an input. (b) Write a Matlab script entitled "myplot.m” that plots the functions f(x) within the interval (-4, 6) using 100000 samples. Use the command "linspace" to generate the x-vector, and the command "plot" to plot the graph. Find the location of the roots within the interval [-4, -1] and [-1,6] using the "zoom-button" in the figure. (c) Write a Matlab function that carries out the False Position method within the interval [a, b] over "n" iterations, where "n" is an input and "a and b" are both inputs and outputs i.e. the function changes the values of "a and b” and returns them at the output. (d) Write a Matlab script that applies 7 iterations of the False Position for the interval (-4,-1) as well as 200 iterations of the for the interval [-1 6]. for loops if-statements How to create Matlab functions and Matlab scripts Understand the mathematics behind "False Position" How to adjust X_upper and x_lower If-decision need to work for both positive and negative slopes Submission DEADLINE: Monday 6pm The WILLIAM

Answer 1

`Hey,

Note: Brother if you have any queries related the answer please do comment. I would be very happy to resolve all your queries.

clc
clear all
close all
x=linspace(-4,6,100000);
y=fun(x);
plot(x,y);
disp('Roots are');
r=falsepos(@fun,-4,-1,1e-17,7)
r=falsepos(@fun,-1,6,1e-17,200)
function y=fun(x)
y=sin(2*pi*x/5)+exp(x/5);
end
function [root,errs, iter]=falsepos(func,lb,ub,err_max,iter_max)
errs=[];
root=[]; func_val=[]; err=[]; numIter=[]; % Output set to empty matricesinitially
exitFlag=1;

if(nargin)==3 % check if last two arguments have been passed or not
err_max=0.0001; % assign the default values
iter_max=50;
elseif (nargin)==4 % check if last argument have been passed or not
iter_max=500; % assign the default values
elseif (nargin)<3 || nargin>5 % if less than three or more than five arguments have been passed, raise an error and return
warning('Insufficient arguments passed!');
return;
  
end

if func(lb)*func(ub)>0 % check if the function value at initial points are not same sign, raise and error return
disp('Probelm with interval signs. Try again!');
exitFlag=-1;
return;
elseif (lb>ub) % check if x_min<x_max i.e. intervals ae not in same order,raise and error return
disp('Probelm with interval size. Try again!');
exitFlag=-1;
return;
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% MAIN BODY OF FUNCTION:

n=0; % number of iteartions computed yet
func_x_max=func(ub); func_x_min=func(lb);

c=lb-((ub-lb)/(func_x_max-func_x_min))*func_x_min; % find the next guess point
err = abs(ub-lb); % take initial error estimate

% Uncomment the following line and line 72 to see result in each iteration
% fprintf('Iteration x_min x_max Root Error estimated ');
while err > err_max && n<iter_max % loop will continue as long as this criteria holds true
n=n+1; % iteration number
if func(lb)*func(c)<0 % select the interval of root
ub = c;
  
else % select the interval of root
lb = c;
end
func_x_max=func(ub); func_x_min=func(lb);
  
c = lb-((ub-lb)/(func_x_max-func_x_min))*func_x_min; % find the next guess point
err = abs(ub-lb)/abs(ub);
errs(n)=err;
% Uncomment the following line to see result in each iteration
% fprintf('%d %3.6f %3.4f %3.4f %3.8f ',n,lb,ub,c,err); % display the iteration result
end
root=c;
ea=err;
iter=n;
end

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Kindly revert for any queries

Thanks.