Implement the Eulers method in MATLAB and solve the problem

Implement the Euler’s method in MATLAB and solve the problem y\'=x^2+y^2; y(0) = 4, using different steps for the approximation. Plot the results.

Step Sizes: .1,.05,.025.01

Solution

[1]

h=0.1; % step\'s size

N=10; % number of steps

y(1)=4;

x(1)=4;

for n=1:N

y(n+1)= y(n)+ h*(y(n).^2 + x(n).^2);

x(n+1)= x(n).^2 + h;

end

plot(x,y)

[2]

h=0.05; % step\'s size

N=10; % number of steps

y(1)=4;

x(1)=4;

for n=1:N

y(n+1)= y(n)+ h*(y(n).^2 + x(n).^2);

x(n+1)= x(n).^2 + h;

end

plot(x,y)

[3]

h=0.25; % step\'s size

N=10; % number of steps

y(1)=4;

x(1)=4;

for n=1:N

y(n+1)= y(n)+ h*(y(n).^2 + x(n).^2);

x(n+1)= x(n).^2 + h;

end

plot(x,y)

[4]

h=0.01; % step\'s size

N=10; % number of steps

y(1)=4;

x(1)=4;

for n=1:N

y(n+1)= y(n)+ h*(y(n).^2 + x(n).^2);

x(n+1)= x(n).^2 + h;

end

plot(x,y)