Question

Differential Equation in matlab:

Please help!

Thanks

2. (30 pts.) Implement the Euler's method in MATLAB and solve the problem y a2+ y(0) 4, using different steps for the approximation. Plot the results.

Answer 1

Matlab code for different steps:

% Euler's Methode
close all
clc;
clear all;
h = 0.2;
y(1) = 4;
x = 0:0.2:2;
for n = 1:size(x,2)-1
y(n+1) = y(n) + h*( (x(n))^2 + (y(n))^2 );
end

plot(x,y)
xlabel('t');
ylabel('y');

hold on

clear all;
h = 0.2;
y(1) = 4;
x = 0:0.02:2;
for n = 1:size(x,2)-1
y(n+1) = y(n) + h*( (x(n))^2 + (y(n))^2 );
end

plot(x,y)
xlabel('t');
ylabel('y');

hold on

clear all;
h = 0.2;
y(1) = 4;
x = 0:0.002:2;
for n = 1:size(x,2)-1
y(n+1) = y(n) + h*( (x(n))^2 + (y(n))^2 );
end

plot(x,y)
xlabel('t');
ylabel('y');

legend('h = 0.2', 'h=0.02', 'h = 0.002');

Plot obtained from euler's methode:

2e+156 h 0.02 h . 002 1.5e+156 1e+156 >1e+156 5e+155 0.5 1.5

Actual plot of the exact solution:

1-65 4.5 0.5 0.5 1.5 2.5 3.5 4.5