Question

Solve y'=4-t+2y; y(0)=1. Generate data-point solutions for t=0,1,2,3,4,5

(i) Stepsize h=0.1

(ii) Stepsize h=0.01

Answer 1

% We will solve this problem by Euler's Method

clc;

clear all;

c=1;

h = 0.1; % initial step size

for j=1:2

t = 0:h:5; % the range of t

y = zeros(size(t)); % allocate the result y

y(1) = 1; % the initial y value

n = numel(y); % the number of y values

% The loop to solve the ODE

for i=1:n-1

f = 4-t(i)+2*y(i); % The given function

y(i+1) = y(i) + h * f; % formula for Euler's method.

end

fprintf('The solutions with step size %f\n',h)

fprintf('t \t y(t)\n')

fprintf('------------------------------\n')

a=0;

b=1;

for i=1:6

fprintf('%.0f \t %f\n',a,y(b))

a=a+1;

b=b+(c*10);

end

h=h*0.1;

c=10;

end