Related papers: A novel second order finite difference discrete sc…
We propose a novel numerical algorithm utilizing model reduction for computing solutions to stationary partial differential equations involving the spectral fractional Laplacian. Our approach utilizes a known characterization of the…
A fractional Hamiltonian formalism is introduced for the recent combined fractional calculus of variations. The Hamilton-Jacobi partial differential equation is generalized to be applicable for systems containing combined Caputo fractional…
A fractal mobile-immobile (MIM in short) solute transport model in porous media is set forth, and an inverse problem of determining the fractional orders by the additional measurements at one interior point is investigated by Laplace…
In this work, we investigate a linear differential equation involving Caputo-Fabrizio fractional derivative of order $1<\beta\leq 2$. Under some assumptions the considered equation is reduced to an integer order differential equation and…
In this paper, we introduce a novel category of central compact schemes inspired by existing cell-node and cell-centered compact finite difference schemes, that offer a superior spectral resolution for solving the dispersive wave equation.…
We propose a fourth--order compact finite--difference (HOC--FD) scheme for the transformed Bates partial integro--differential equation (PIDE). The method employs an implicit--explicit (IMEX) Crank--Nicolson framework for local terms and…
The implicit compact finite-difference scheme was developed for evolutionary partial differential parabolic and Schr\"odinger-type equations and systems with a weak nonlinearity. To make a temporal step of the compact implicit scheme we…
This paper proposes a new numerical method based on the Chebyshev wavelets (CWs) to solve the variable-order time fractional mobile-immobile advection-dispersion equation. To do this, a new operational matrix of variable-order fractional…
In this paper, we consider a fast and second-order implicit difference method for approximation of a class of time-space fractional variable coefficients advection-diffusion equation. To begin with, we construct an implicit difference…
This paper introduces a novel approach for the construction of bulk--surface splitting schemes for semi-linear parabolic partial differential equations with dynamic boundary conditions. The proposed construction is based on a reformulation…
In molecular dynamics, transport coefficients measure the sensitivity of the invariant probability measure of the stochastic dynamics at hand with respect to some perturbation. They are typically computed using either the linear response of…
We prove existence and uniqueness of the flow of water within a confined aquifer with fractional diffusion in space and fractional time derivative in the sense of Caputo-Fabrizio. Our main method is the fixed-point theorem. We propose the…
In this paper, we propose a time-fractional molecular beam epitaxy (MBE) model with slope selection and its efficient, accurate, full discrete, linear numerical approximation. The numerical scheme utilizes the fast algorithm for the Caputo…
For $0<\nu_2<\nu_1\leq 1$, we analyze a linear integro-differential equation on the space-time cylinder $\Omega\times(0,T)$ in the unknown $u=u(x,t)$ $$\mathbf{D}_{t}^{\nu_1}(\varrho_{1}u)-\mathbf{D}_{t}^{\nu_2}(\varrho_2…
In this note, we prove or re-prove several important results regarding one dimensional time fractional ODEs following our previous work \cite{fllx17}. Here we use the definition of Caputo derivative proposed in \cite{liliu17frac1,liliu2017}…
Recently a useful finite-difference scheme was proposed in [Phys. Rev. E 98, 033302 (2018)] to solve Fokker-Planck equations with drift-admitting jumps. However, while the scheme is fifth order for the case with smooth drifts, it is only…
In this article, a high-order time-stepping scheme based on the cubic interpolation formula is considered to approximate the generalized Caputo fractional derivative (GCFD). Convergence order for this scheme is $(4-\alpha)$, where $\alpha…
As we are aware, various types of methods have been proposed to approximate the Caputo fractional derivative numerically. A common challenge of the methods is the non-local property of the Caputo fractional derivative which leads to the…
Monte Carlo approaches to radiation transport have several attractive properties such as simplicity of implementation, high accuracy, and good parallel scaling. Moreover, Monte Carlo methods can handle complicated geometries and are…
In this paper, we consider numerical approximation of an electrically conductive ferrofluid model, which consists of Navier-Stokes equations, magnetization equation, and magnetic induction equation. To solve this highly coupled, nonlinear,…