A Polynomial Based Iterative Method for Linear Parabolic Equations

A new polynomial based method (PBM) is developed to integrate multi-dimensional linear parabolic initial-boundary-value problems. It is based on $L\sb2$-approximations to $f(z) = (1 - exp(-z))/z,f(0) = 1,$ over ellipses in the complex plane using expansions of f in Chebychev polynomials. The calculation of the Fourier Coefficients requires numerical integration over only a single line segment in the complex plane whose length and orientation depend on the step size and the parabolic operator itself. The simplicity with which these coefficients are obtained rests on special properties of the Chebychev polynomials.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Schaefer, Mark Johannes

• Computer Science

Identifier

(UMI)AAI8721754

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/69578