Consider this differential equation,
$dy/dx = x + \sin(y)$
with initial condition $y = 0.5$ when $x = 1.2$:
- Write down the recurrence relation for Euler's numerical method applied above.
- With step size h = 0.1, calculate the approximations to y(1.3) and y(1.4).
This is my answer:
$$Y_i+1 = Y_i + 0.1(X_i + \sin(Y_i))$$
I have problem solving this one...
From my txtbk reference, I sub $i = 1$ into the eqn thus giving me
$Y_1 = Y_0 + 0.1(1.2 + \sin(0.5)) = 0.1679$
Then, $i = 2$
$Y_2 = Y_1 + 0.1(1.3 + \sin(0.6)$
Im sure my method in part 2 is wrong and I don't really understand how to solve it via my txtbk.