hmwk_5_2010

# B using interpolating polynomials since we can

• Notes
• 3

This preview shows page 1 - 2 out of 3 pages.

b) Using Interpolating polynomials; Since we can estimate the p th derivative of f(x) simply by differentiating: . We can apply any of our methods to derive the interpolating func- tion and its error. We then differentiate and evaluate at the left most point in order to derive a forward differ- ence approximation, at the right most point to derive a backward difference approximation and at the center point in order to derive a central difference approximation. c) We can apply difference operators (forward, central, backward); we can average forward and backward difference operators, or apply combined forward and backward operators. The order of the leading n th order error term (if it in fact dominates and we are in the so called asymptotic range) controls how fast the solution converges as space or time resolution is reduced. On a log error vs. log grid spacing plot, the error curve will have a slope equal to n . Higher order methods can be applied to help reduce the cost of the computational solutions, since higher order methods can apply larger grid spacing and therefore fewer computational points for equivalent accuracy as compared to lower order methods. Problem 1 Use the method of undetermined coefficients to derive a fourth order accurate central difference approximation

Subscribe to view the full document.

You've reached the end of this preview.

{[ 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