Semi-implicit Hermite–Galerkin Spectral Method for Distributed-Order Fractional-in-Space Nonlinear Reaction–Diffusion Equations in Multidimensional Unbounded Domains

A linearized finite difference/spectral-Galerkin scheme for three-dimensional distributed-order time–space fractional nonlinear reaction–diffusion-wave equation: Numerical simulations of Gordon-type solitons

(2020) Shimin Guo et al.   COMPUTER PHYSICS COMMUNICATIONS

Finite difference/Hermite-Galerkin spectral method for multi-dimensional time-fractional nonlinear reaction-diffusion equation in unbounded domains

(2019) Shimin Guo et al.   APPLIED MATHEMATICAL MODELLING

Multi-domain spectral collocation method for variable-order nonlinear fractional differential equations

(2019) Tinggang Zhao et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

An unstructured mesh finite element method for solving the multi-term time fractional and Riesz space distributed-order wave equation on an irregular convex domain

(2019) Y.H. Shi et al.   APPLIED MATHEMATICAL MODELLING

Space-time finite element method for the distributed-order time fractional reaction diffusion equations

(2019) Weiping Bu et al.   APPLIED NUMERICAL MATHEMATICS

An efficient split-step method for distributed-order space-fractional reaction-diffusion equations with time-dependent boundary conditions

(2019) Kamran Kazmi et al.   APPLIED NUMERICAL MATHEMATICS

What is the fractional Laplacian? A comparative review with new results

(2019) Anna Lischke et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Anomalous diffusion in comb model subject to a novel distributed order time fractional Cattaneo–Christov flux

(2019) Lin Liu et al.   APPLIED MATHEMATICS LETTERS

Finite difference/spectral-Galerkin method for a two-dimensional distributed-order time–space fractional reaction–diffusion equation

(2018) Shimin Guo et al.   APPLIED MATHEMATICS LETTERS

A numerical method for solving the two-dimensional distributed order space-fractional diffusion equation on an irregular convex domain

(2018) Wenping Fan et al.   APPLIED MATHEMATICS LETTERS

A fast finite difference method for distributed-order space-fractional partial differential equations on convex domains

(2018) Jinhong Jia et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Fractional spectral and pseudo-spectral methods in unbounded domains: Theory and applications

(2017) Hassan Khosravian-Arab et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Computing Fractional Laplacians on Complex-Geometry Domains: Algorithms and Simulations

(2017) Fangying Song et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Hermite Spectral Methods for Fractional PDEs in Unbounded Domains

(2017) Zhiping Mao et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

A fractional phase-field model for two-phase flows with tunable sharpness: Algorithms and simulations

(2016) Fangying Song et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Spectral direction splitting methods for two-dimensional space fractional diffusion equations

(2015) Fangying Song et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Fractional Sturm–Liouville boundary value problems in unbounded domains: Theory and applications

(2015) Hassan Khosravian-Arab et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Artificial boundary conditions and finite difference approximations for a time-fractional diffusion-wave equation on a two-dimensional unbounded spatial domain

(2014) Hermann Brunner et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A Fourth-order Compact ADI scheme for Two-Dimensional Nonlinear Space Fractional Schrödinger Equation

(2014) Xuan Zhao et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

A finite difference scheme for fractional sub-diffusion equations on an unbounded domain using artificial boundary conditions

(2012) Guang-hua Gao et al.   JOURNAL OF COMPUTATIONAL PHYSICS

The finite difference approximation for a class of fractional sub-diffusion equations on a space unbounded domain

(2012) Guang-hua Gao et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Numerical analysis for distributed-order differential equations

(2008) Kai Diethelm et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Connection coefficients between orthogonal polynomials and the canonical sequence: an approach based on symbolic computation

(2008) P. Maroni et al.   NUMERICAL ALGORITHMS