Euler Function

Create a file called euler.m that contains a function of the form

function $[t,y]=$ euler$($f$,$ t$0,$ y$0,$ tn$,$ N$)$

This function should accept

f : an anonymous function $($help on anonymous functions$)$ of $t$ and $y$ that describes the differential equation,

such that $y^{\text{'}}=f(t,y)$

$($use $f=$@$(t,y)dots$ to define it$,$ but that comes later$)$

t$0,$ y$0$: the initial condition

tn: the $t$ value where the approximation should end

N : the number of steps used to get from to to tn

It should return

t: an array containing $N+1$ values, evenly spaced from to to tn

y: an array representing the solution to the differential equation $($the final value should be $y(t_n))$

Start by using to$,$ tn$,$ and N to calculate the step size h $,$ then use that to generate the t array. Once you have

that, initialize the y array $($I usually start by creating an array of zeros of the right size$).$

Then use a for loop to fill in the values in the y array, using the formula for Euler's method $($inside the loop,

calculate the value of the derivative at that point and use that to get the next $y$ value$).$