SPECTRAL METHODS FOR FRACTIONAL LAPLANCIAN

Huang, Zitai; Sun, Shuyang

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SPECTRAL METHODS FOR FRACTIONAL LAPLANCIAN Public

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.

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