# Math Help - Numerical Approximatin: Euler's Method

1. ## Numerical Approximatin: Euler's Method

These problem are also due in two days. I just wanted to post them separately because they're two different subjects.Thanks.

1) Apply Euler's Method with h=0.1 to approximate the solution of the initial value problem ==> y'= y- x- 1, y(o)=1 <=== on the interval [0, 1/2]

2) Apply Euler's Method with h=0.25 to approximate the solution of the initial value problem ==> y'=y- x- 1, y(0)=1 <=== on the interval [0, 1/2]

3) Given the initial value problem: dy/dx= y, y(0)= 1. Do the following:

a. Solve the initial value problem and show that e= y(1).
b. Apply Euler's Method with h= 0.25 to approximate e= y(1).
c. Apply improved Euler's Method with h=0.5 to approximate e=y(1).
d. Apply Runge-Kutta Method with h=1 to approximate e= y(1).
e. Find errors of the above approximations of e. Wich approximation is the best?

2. Originally Posted by googoogaga
These problem are also due in two days. I just wanted to post them separately because they're two different subjects.Thanks.

1) Apply Euler's Method with h=0.1 to approximate the solution of the initial value problem ==> y'= y- x- 1, y(o)=1 <=== on the interval [0, 1/2]
see attachment.

RonL

3. ## I have no clue of what that means.

Could you please explain in lamer terms?

4. Originally Posted by googoogaga
Could you please explain in lamer terms?
First col contains $x_0, x_1, ..,$ third col is $y'(x_n)$, first element of second
col is $y(x_0)$, subsequent terms are $y(x_{n-1})+hy'(x_{n-1}), h=delta\_x$

RonL