Computing solution landscape of nonlinear space-fractional problems via fast approximation algorithm

by   Bing Yu, et al.
Peking University

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.


A fast method for variable-order space-fractional diffusion equations

We develop a fast divided-and-conquer indirect collocation method for th...

On Generalisation of Isotropic Central Difference for Higher Order Approximation of Fractional Laplacian

The study of generalising the central difference for integer order Lapla...

Convergence analysis of variable steps BDF2 method for the space fractional Cahn-Hilliard model

An implicit variable-step BDF2 scheme is established for solving the spa...

Numerical Approximation of the Fractional Laplacian on R Using Orthogonal Families

In this paper, using well-known complex variable techniques, we compute ...

On the two-phase fractional Stefan problem

The classical Stefan problem is one of the most studied free boundary pr...

Please sign up or login with your details

Forgot password? Click here to reset