Related papers: Polynomial Spectral collocation Method for Space F…
We presented a general approach for obtaining the generalized transport equations with fractional derivatives by using the Liouville equation with fractional derivatives for a system of classical particles and Zubarev's nonequilibrium…
We apply the semi-discrete method, c.f. \emph{N. Halidias and I.S. Stamatiou (2016), On the numerical solution of some non-linear stochastic differential equations using the semi-discrete method, Computational Methods in Applied…
We propose a novel and simple spectral method based on the semi-discrete Fourier transforms to discretize the fractional Laplacian $(-\Delta)^\frac{\alpha}{2}$. Numerical analysis and experiments are provided to study its performance. Our…
We construct flexible spatio-temporal models through stochastic partial differential equations (SPDEs) where both diffusion and advection can be spatially varying. Computations are done through a Gaussian Markov random field approximation…
A spectral method is considered for approximating the fractional Laplacian and solving the fractional Poisson problem in 2D and 3D unit balls. The method is based on the explicit formulation of the eigenfunctions and eigenvalues of the…
A spectral solution method is proposed to solve a previuously developed non-equilibrium statistical model describing partial thermalization of produced charged hadrons in relativistic heavy-ion collisions, thus improving the accuracy of the…
We investigate evolution equations for anomalous diffusion employing fractional derivatives in space and time. Linkage between the space-time variables leads to a new type of fractional derivative operator. Fractional diffusion equations…
We examine the spectral structure of the two-dimensional advection-diffusion operator in flows with mixed phase space at very large Peclet number. Using Fourier discretization combined with symmetry reduction and Krylov-Arnoldi methods, we…
The paper provides the fractional integrals and derivatives of the Rie\-mann-Liouville and Caputo type for the five kinds of radial basis functions (RBFs), including the powers, Gaussian, multiquadric, Matern and thin-plate splines, in one…
Fractional kinetic equations employ non-integer calculus to model anomalous relaxation and diffusion in many systems. While this approach is well explored, it so far failed to describe an important class of transport in disordered systems.…
We propose a second order exponential scheme suitable for two-component coupled systems of stiff evolutionary advection--diffusion--reaction equations in two and three space dimensions. It is based on a directional splitting of the involved…
This paper establishes explicit solutions for fractional diffusion problems on bounded domains. It also gives stochastic solutions, in terms of Markov processes time-changed by an inverse stable subordinator whose index equals the order of…
This work explores different particle-based approaches to the simulation of one-dimensional fractional subdiffusion equations in unbounded domains. We rely on smooth particle approximations, and consider four methods for estimating the…
We comparatively use some classical spectral collocation methods as well as highly performing Chebfun algorithms in order to compute the eigenpairs of second order singular Sturm-Liouville problems with separated self-adjoint boundary…
Fractional diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogues. They are used in physics to model anomalous diffusion. This paper develops strong solutions of space-time fractional…
This article is in continuation of our earlier article [37] in which computational solution of an unified reaction-diffusion equation of distributed order associated with Caputo derivatives as the time-derivative and Riesz-Feller derivative…
Nowadays, fractional differential equations are a well established tool to model phenomena from the real world. Since the analytical solution is rarely available, there is a great effort in constructing efficient numerical methods for their…
High-dimensional Partial Differential Equations (PDEs) are a popular mathematical modelling tool, with applications ranging from finance to computational chemistry. However, standard numerical techniques for solving these PDEs are typically…
In this paper, we consider the initial boundary value problem of the two dimensional multi-term time fractional mixed diffusion and diffusion-wave equations. An alternating direction implicit (ADI) spectral method is developed based on…
Based on the superconvergent approximation at some point (depending on the fractional order $\alpha$, but not belonging to the mesh points) for Gr\"{u}nwald discretization to fractional derivative, we develop a series of high order…