Question

Use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated value. First use

h = 0.1

and then use

h = 0.05.

y' = y − y², y(0) = 0.3;    y(0.5)

4. 0/1 points Previous Answers ZillDiffEQ ModAp 11M 2.6.010. My Notes Ask Your Teacher Use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. y' = y - y2, 7(0) = 0.3; y(0.5) y(0.5) < 0.7956 x (h = 0.1) y(0.5) - 0.75019 X (n = 0.05) Need Help? Watch It Viewing Saved Work Revert to Last Response Submit Answer Practice Another Version

Answer 1

MATLAB Script:

close all
clear
clc

f = @(x,y) y - y^2; % Given ODE
x0 = 0; xf = 0.5; % Intervals of x
y0 = 0.3; % Initial condition

h1 = 0.1; % Step Size 1
y1 = euler(x0, y0, xf, h1, f);
fprintf('For h = 0.1, y(0.5) = %.4f\n', y1(end))

h2 = 0.05; % Step Size 2
y2 = euler(x0, y0, xf, h2, f);
fprintf('For h = 0.05, y(0.5) = %.4f\n', y2(end))

function y = euler(x0, y0, xf, h, f)
y(1) = y0;
x = x0:h:xf;
for i = 1:length(x)-1
f1 = f(x(i), y(i));
y(i+1) = y(i) + h*f1; % Euler's Update
end
end

Output:

For h = 0.1, y(0.5) = 0.4123
For h = 0.05, y(0.5) = 0.4132