Related papers: On a collocation method for the time-fractional co…
In this paper, we propose high order numerical methods to solve a 2D advection diffusion equation, in the highly oscillatory regime. We use an integrator strategy that allows the construction of arbitrary high-order schemes {leading} to an…
We study an approximation method to solve nonlinear multi-term fractional differential equations with initial conditions or boundary conditions. First, we transform the nonlinear multi-term fractional differential equations with initial…
In this paper, we propose a new approach, based on the so-called modulating functions to estimate the average velocity, the dispersion coefficient and the differentiation order in a space fractional advection dispersion equation. First, the…
The fundamental solution of the fractional diffusion equation of distributed order in time (usually adopted for modelling sub-diffusion processes) is obtained based on its Mellin-Barnes integral representation. Such solution is proved to be…
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…
In this paper, we propose an efficient numerical scheme for the approximate solution of the time fractional diffusion-wave equation with reaction term based on cubic trigonometric basis functions. The time fractional derivative is…
A recent development in the theory of fractional differential equations with variable coefficients has been a method for obtaining an exact solution in the form of an infinite series involving nested fractional integral operators. This…
In this paper, we develop a robust fast method for mobile-immobile variable-order (VO) time-fractional diffusion equations (tFDEs), superiorly handling the cases of small or vanishing lower bound of the VO function. The valid fast…
We explain how the invariant subspace method can be extended to a scalar and coupled system of time-space fractional partial differential equations. The effectiveness and applicability of the method have been illustrated through time-space…
Space fractional convection diffusion equation describes physical phenomena where particles or energy (or other physical quantities) are transferred inside a physical system due to two processes: convection and superdiffusion. In this…
This paper represents a mixed numerical method for the multi-resolution solution of non-linear partial differential equations based on B-Spline wavelets. The method is based on a second-order finite difference formula combined with the…
In this paper, an efficient numerical technique for the time-fractional telegraph equation is proposed. The aim of this paper is to use a relatively new type of B-spline called the cubic trigonometric B-splines for the proposed scheme. This…
We investigate diffusion equations with time-fractional derivatives of space-dependent variable order. We examine the well-posedness issue and prove that the space-dependent variable order coefficient is uniquely determined among other…
A hybridized discontinuous Galerkin method is proposed for solving 2D fractional convection-diffusion equations containing derivatives of fractional order in space on a finite domain. The Riemann-Liouville derivative is used for the spatial…
We begin with a treatment of the Caputo time-fractional diffusion equation, by using the Laplace transform, to obtain a Volterra intego-differential equation where we may examine the weakly singular nature of this convolution…
In this work, we construct novel discretizations for the unsteady convection-diffusion equation. Our discretization relies on multiderivative time integrators together with a novel discretization that reduces the total number of unknowns…
We study a second order scheme for spatial fractional differential equations with variable coefficients. Previous results mainly concentrate on equations with diffusion coefficients that are proportional to each other. In this paper, by…
We propose a collocation method based on multivariate polynomial splines over triangulation or tetrahedralization for the numerical solution of partial differential equations. We start with a detailed explanation of the method for the…
We propose a high-order spacetime wavelet method for the solution of nonlinear partial differential equations with a user-prescribed accuracy. The technique utilizes wavelet theory with a priori error estimates to discretize the problem in…
The work presents integral solutions of the fractional subdiffusion equation by an integral method, as an alternative approach to the solutions employing hypergeometric functions. The integral solution suggests a preliminary defined profile…