HW_07_Solutions

# HW_07_Solutions - A Problem 1 Eulers method(a The true...

This preview shows pages 1–2. Sign up to view the full content.

A. Problem 1. Euler’s method (a) The true solution, Y(x), is only given as a reference for the obtained numerical solutions. Thus, we have to avoid any kind of substitutions of the given true soution into Euler equation or the given diﬀerential equation. Y 0 = [ cos ( Y ( x ))] 2 , 0 x 0 . 5 , Y (0) = 0 , h = 0 . 1 Y ( x ) = tan - 1 ( x ) x n +1 = x n + h, y n +1 = y n + hy 0 ( x n , y n ) = y n + h [ cos ( y ( x n ))] 2 , Y ( x ) = tan - 1 ( x ) x 0 = 0 , y 0 = 0 , error = y ( x n ) - Y ( x n ) x 1 = 0 . 1 , y 1 = 0 + 0 . 1 · cos 2 (0) = 0 . 1 , Y (0 . 1) = 0 . 0997 , error = 0 . 0003 x 2 = 0 . 2 , y 2 = 0 . 1 + 0 . 1 · cos 2 (0 . 1) = 0 . 199003 , Y (0 . 2) = 0 . 197 , error = 0 . 002003 x 3 = 0 . 3 , y 3 = 0 . 199003 + 0 . 1 · cos 2 (0 . 199003) = 0 . 295095 , Y (0 . 3) = 0 . 291 , error = 0 . 004095 x 4 = 0 . 4 , y 4 = 0 . 295095 + 0 . 1 · cos 2 (0 . 295095) = 0 . 386637 , Y (0 . 4) = 0 . 381 , error = 0 . 005637 x 5 = 0 . 5 , y 5 = 0 . 386637 + 0 . 1 · cos 2 (0 . 386637) = 0 . 472418

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

HW_07_Solutions - A Problem 1 Eulers method(a The true...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online