Computing solution landscape of nonlinear space-fractional problems via fast approximation algorithm
Abstract
The nonlinear space-fractional problems often allow multiple stationary solutions, which can be much more complicated than the corresponding integer-order problems. In this paper, we systematically compute the solution landscapes of nonlinear constant/variable-order space-fractional problems. A fast approximation algorithm is developed to deal with the variable-order spectral fractional Laplacian by approximating the variable-indexing Fourier modes, and then combined with saddle dynamics to construct the solution landscape of variable-order space-fractional phase field model. Numerical experiments are performed to substantiate the accuracy and efficiency of fast approximation algorithm and elucidate essential features of the stationary solutions of space-fractional phase field model. Furthermore, we demonstrate that the solution landscapes of spectral fractional Laplacian problems can be reconfigured by varying the diffusion coefficients in the corresponding integer-order problems.
Cite
@article{arxiv.2108.03141,
title = {Computing solution landscape of nonlinear space-fractional problems via fast approximation algorithm},
author = {Bing Yu and Lei Zhang and Pingwen Zhang and Xiangcheng Zheng},
journal= {arXiv preprint arXiv:2108.03141},
year = {2022}
}