Question

Numerical Analysis:

Make a matlab code that computes the Modified Euler's method for a given function y' =  t + y from 0 < t < 4 (inclusive) with h=0.5 and with initial condition y(0) = 0.
Please make output display in tabular form and not in a plot, that doesn't help show the actual values.

Answer 1

MATLAB CODE

clc;
a=0;
b=4;
h=0.5;
N=(b-a)/h;
t=[a:h:b];
y(1)=0;
for i=1:N
y(i+1)=y(i)+h*(t(i)+y(i));
y(i+1)=y(i)+h/2*(t(i)+y(i)+t(i+1)+y(i+1));
end
t
y

ANSWERS

t =

0 0.5000 1.0000 1.5000 2.0000 2.5000 3.0000 3.5000 4.0000

y =

0 0.1250 0.6406 1.7910 3.9729 7.8310 14.4128 25.4208 43.6213