157_pdfsam_math 54 differential equation solutions odd

# 157_pdfsam_math 54 differential equation solutions odd -...

This preview shows page 1. Sign up to view the full content.

Exercises 3.7 n = 0 , 1 , 2 , . . ., 35.) Lastly, we redo this work with K = 0 . 6 and h = 2 / 3. By so doing, we obtain the results given in the table in the answers of the text. (Note that the values for T 0 , T 6 , T 12 , T 18 , T 24 , T 30 , and T 36 are given in the answers.) EXERCISES 3.7: Higher Order Numerical Methods: Taylor and Runge-Kutta, page 142 1. In this problem, f ( x, y ) = cos( x + y ). Applying formula (4) on page 135 of the text we compute ∂f ( x, y ) ∂x = ∂x [cos( x + y )] = sin( x + y ) ∂x ( x + y ) = sin( x + y ); ∂f ( x, y ) ∂y = ∂y [cos( x + y )] = sin( x + y ) ∂y ( x + y ) = sin( x + y ); f 2 ( x, y ) = ∂f ( x, y ) ∂x + ∂f ( x, y ) ∂y f ( x, y ) = sin( x + y ) + [ sin( x + y )] cos( x + y ) = sin( x + y )[1 + cos( x + y )] , and so, with p = 2, (5) and (6) on page 135 yield x n +1 = x n + h ,
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern