# Numerical Approximatin: Euler's Method

• Jul 19th 2007, 08:01 AM
googoogaga
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?
• Jul 19th 2007, 11:46 AM
CaptainBlack
Quote:

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
• Jul 20th 2007, 07:35 AM
googoogaga
I have no clue of what that means.
:confused: Could you please explain in lamer terms?
• Jul 20th 2007, 10:17 AM
CaptainBlack
Quote:

Originally Posted by googoogaga
:confused: Could you please explain in lamer terms?

First col contains \$\displaystyle x_0, x_1, ..,\$ third col is \$\displaystyle y'(x_n)\$, first element of second
col is \$\displaystyle y(x_0)\$, subsequent terms are \$\displaystyle y(x_{n-1})+hy'(x_{n-1}), h=delta\_x\$

RonL