Question

3. Constler the folloving nitial valse proble dy Take one stop of the modified Euler8 nelloul Un+,-di +습 (J(z",la) + f(m+1 lat)) with h 0.2 o find the approximate value of g/(1.2). (Hint: set up the equation for lh and use the fsolne Matlab fnnetion to solve for ) (working space if required) gSofue (@ (K) γ-1-0.1 (asasteos('.2, 02 e oudit

i need the code for this question please

Answer 1

MATLAB Code:

close all
clear
clc

x0 = 1;
y0 = 1; % y(1) and y1 = y(1.2)
h = 0.2;
x1 = x0 + h;
f = @(x,y) cos(x*y);
eqn = @(y1) y1 - ( y0 + (h/2) * (f(x0,y0) + f(x1,y1)) ); % eqn. that needs to be solved
y1 = fsolve(eqn, 0); % with initial guess of y1 = 0
disp('y(1.2) ='), disp(y1)

Output:

y(1.2) =
1.0810