Question

Design Layout References Mailings Review View Share 1) (15 points) Calculate the following for the function f(x) = e-a-x a. Use calculus to determine the correct value of the derivative. b. Develop an M-file function to evaluate the centered finite-difference approximations, starting with x = 0.5 Thus, for the first evaluation, the x values for the centered difference approximation will be x-2 ± 0.5 or x 1.5 and 2.5. Then, decrease in increments of 0.1 down to a minimum value of x = 0.01 c. Repeat part (b) for the second-order forward and backward differences. (Note that these can be done at the same time that the centered difference is computed in the loop.) d. Plot the results of (b) and (c) versus x. On the same plot also show the true value of the derivative for the range of 0 to 0.5. Use the following formulas: Centered diff. df/dx (f (i+1)-f (i-1))/2d:x Fwd. diff Bkwd. diff. df/dx- (3f (i)-4f (i-1) +f (i-2))/2dx df/dx-(-f (i+2) +4f (i+1)-3f (i))/2dx 따 English (United States) O Focus

please i need the requiered MATLAB script to solve this. All calculations need to be done in matlab please

Answer 1

`Hey,

Note: Brother in case of any queries, just comment in box I would be very happy to assist all your queries

clc
%%Matlab code for forward backward and central difference method
clear all
close all

%function for which derivative have to find
f=@(x) exp(-2*x)-x;

%Function for exact derivative of function
df=@(x) (-2*exp(-2*x))-1;

%exact solution for f'(x) at x=2
ext_val=df(2);

%x value at which derivative have to find
x0=2;

%all h values
hh=linspace(0.5,0.01,40);
%loop for forward backward and central difference formulae
fprintf('\th,\tcntrl_diff,\tfrwd_diff,\tbkwd_diff\n')
for i=1:length(hh)
%all step size
h=hh(i);
%central diff
cn_frwd(i)=(f(x0+h)-f(x0-h))/(2*h);
  
%forward diff
fd_frwd(i)=(-f(x0+2*h)+4*f(x0+h)-3*f(x0))/(2*h);
%backward diff
bk_frwd(i)=(3*f(x0)-4*f(x0-h)+f(x0-2*h))/(2*h);
%exaxt differential
ext_diff(i)=ext_val;
  
%printing the result
fprintf('\t%.2f, \t%.4f, \t %.4f, \t %.4f.\n',h,cn_frwd(i),fd_frwd(i),bk_frwd(i))
end
%Loglog plot of true error vs h
plot(hh,cn_frwd,'linewidth',2)
hold on
plot(hh,fd_frwd,'linewidth',2)
plot(hh,bk_frwd,'linewidth',2)
plot(hh,ext_diff,'linewidth',2)

xlabel('step size (h)')
ylabel('numerical differential')
title('numerical differential vs. step size plot')
legend('Central difference','Forward difference','Backward difference','exact differential')

MATLAB R2018a Figure ② ▼| rch Documentation Log In EDITOR nsert Comment Indent Eile Edit Yiew Insert Iools Desktop Window Help Find Files CompareG To Comment% Go To New Open Save Print Find numerical differential vs. step size plot 1.005 Central difference Forward difference Backward difference C: Users PRADEEP KALRA 、Documents 1.01 Current Folder Name mathlab Edit exact differential 41- 1.015 E 43- in 1.02 New folder a1.m 45 46-D o1.025 a4.m a5.m A1.dat A1.mat A2.dat A3.dat 4.dat cxac 1.03 New to 1.035 1.04 Details 1.045 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40.45 0.5 step size (h) Name ▲ Value 40 double x40 double x)-2 exp(-2x))-1 40 double 1.0366 @(x)expl.2x).x x40 double 0.0100 40 double -1.0362, -1.0363, -1.0364, -1.0365 -1.0365, -1.0366, -1.0366, -1.0366, -1.0361 -1.0362 -1.0363. -1.0364 -1.0365. -1.0366 -1.0366. -1.0366 0.10, -1.0369, 0.09. -1.0363, 0.07, -1.0368, 0.06, -1.0367, 0.05,-1.0367, 0.04 -1.0367, 0.02,-1.0366, 0. -1.0366, cn frwd ext_diff ext val fd frwd Ln 48 Coll 93 ^ } ) ENG 12:13 PM IN 05/11/19 O Type here to search

Kindly revert for any queries

Thanks.