Question

Using Matlab, write an .M code program:

Write a program for numerical solution of nonlinear equation by Fixed-Point Iteration method with given accuracy elementof. Solve the equation. Try 3 different representations of the equation in the form x = g(x). For every representation solve the problem with initial approximations x0 = 0, x0 = 2, and x0 = 10 and with the accuracy elementof = 10^-8. f(x) = e^x - 3x^4 - 40x - 10 = 0.

Answer 1

Copyable Code:

%function f(x)

f = @(x)exp(x)-3*x.^4-40*x-10;

% initial value

x0 = 0; %change the value here x0 = 2 and x0 = 10

%initialize the iteration

i = 0;

%initialize the no. of iterations

t_iter = 5;

% initialize array to save iterations

xa = NaN(1,t_iter);

%assign the accuracy

acc = 1e-8;

%initialize the error

x_error = inf;

%check the while loop

while (i < t_iter) && (x_error > acc)

i = i + 1;

x_value = f(x0);

%store every iteration

xa(i) = x_value;

%find difference of initial value and x_value

x_error = abs(x_value - x0);

x0 = x_value;

end

%fixed iteration value

xa = xa(1:i);

%display the all iteration value

fprintf('%15.8e\n', xa);