Abstract

Researchers are interested in three types of error: experimental error, truncation error, and interpolation error. This thesis will study the last. Given a differential equation g"(x) = f(x) and a fixed number of interpolation grid points, an optimation problem is formulated to minimize the difference between f(x) and its interpolating function, thus reducing the error between the actual solution and the approximated solution of the ODE. Using the Nelder-Mead Simplex Method, the optimal distribution of grid points that will minimize the error between the solution g and its approximated solution will be found. This technique will then be applied to the one dimensional light scattering equation gxx = E²x/R. Using the Nelder-Mead Method, the optimal interpolation grid for a given number of grid points will be found. These numerical computations will ultimately be used to give guidance to experimenters on where to take measurements for the Rayleigh Ratio R.

Library of Congress Subject Headings

Differential equations--Numerical solutions; Numerical analysis; Interpolation

Publication Date

5-1-2009

Document Type

Thesis

Department, Program, or Center

School of Mathematical Sciences (COS)

Advisor

Ross, David

Comments

Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works. Physical copy available through RIT's The Wallace Library at: QA299 .M37 2009

Campus

RIT – Main Campus

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