Question

Write MATLAB code

g(x)=x+a*f(x)

f(x)=(e^x)+(x^2)-x-4

function f(x) is stored in fogp1.m

(c) (1) Create a file gopgi.m to calculate the function glir, a) (see Preparation, ex. 7c) function [y] =gopg1(x,a) % input: x, a % output: y y= .....; (2) Create a file sucsub1.m and write a program that calculates the solution using the method of successive substitution. Calculate the values of g(x, a) by making multiple calls to the function gopg1(x, a). Take xo = 1.3 as starting value and try several values for a, including the optimal value that you found (Preparation, ex. 7c). (3) Print the iteration counter at each iteration step, as well as the approximation of the solution. Is your optimal value of a indeed the optimal one? (4) Estimate the error at each iteration by using successive solutions (Preparation, ex. 5a) and use the estimates to determine a stop criterion. The requested accuracy is tol = 10-8

Answer 1

`Hey,

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

clc%clears screen
clear all%clears history
close all%closes all files
format long
x0=1.3;
a=-0.3;
for i=1:100
x1=gopg1(x0,a);
fprintf('Iteration %d, x is %f\n',i,x1);
if(abs((x1-x0)/x0)<1e-8)
break;
end
x0=x1;
end

function y=gopg1(x,a)
y=x+a.*(exp(x)+x.^2-x-4);
end

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Kindly revert for any queries

Thanks.