Question

Find approximate values of the solution of the given initial value problem at T=0.1, 0.2, 0.3, and 0.4 using Euler method with h=0.1

y'= 0.5-t+2y ;   y(o)=1

Answer 1

solution:-

y' = 0.5 - t + 2y      ,    y(0)=1

(a) Find approximate values of the solution of the given initialvalue problem at t = 0.1, 0.2, 0.3, and 0.4 using the Euler methodwith h = 0.1.
%%%%%%%%%

h=0.1;

tmax=0.4;

n=tmax/h;

t(1)= 0;

y(1)=1;

tout=t(1);

yout=y(1).';

disp('ti Euler=y(i) ')

disp('~~~~~~~~~~~~~~~~~~~~~~~~')

for i=1:(n+1)

t(i+1)=t(1)+i*h;

%

k1= h*f(t(i),y(i));

y(i+1)=y(i)+ k1;

tout=[tout;t(i)];

yout=[yout,y(i).'];

fprintf ('%5.2f%17.5f\n',t(i),y(i));

end

////////////////////////////////////////////////////////////////

function yz=f(t,y)

yz= 0.5 - t + 2*y;

/////////////////////////////////////

h=0.1

ti      Euler=y(i)
~~~~~~~~~~~~~~~~~~~~~~~~
0.00         1.00000
0.10         1.25000
0.20         1.54000
0.30         1.87800
0.40         2.27360

NOTE:PLEASE RATE IT