Faculty Advisor

Zhang, Zhongqiang

Abstract

This project is to numerically solve fractional Laplace equations and related equations. The major numerical methods we use are Jacobi-spectral methods. Our ultimate goal is to numerically solve a turbulence testbed problem. To achieve our goal, we first establish fractional Laplacian of Jacobi polynomials and choose proper test functions for our spectral methods. We start from linear steady and unsteady equations and then solve nonlinear unsteady equations. For unsteady equations, we have to take a different test function than that for steady equations to avoid singularity of the resulting linear systems.

Publisher

Worcester Polytechnic Institute

Date Accepted

March 2016

Major

Mathematical Sciences

Project Type

Major Qualifying Project

Accessibility

Unrestricted

Advisor Department

Mathematical Sciences

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