Related papers: Invariant subspace method for (m + 1)-dimensional …
This paper explores variants of the subspace iteration algorithm for computing approximate invariant subspaces. The standard subspace iteration approach is revisited and new variants that exploit gradient-type techniques combined with a…
In this work, we consider an inverse problem of determining a time dependent coefficient in a fully fractional diffusion equation with a nonlinear source term. The nonlocal initial-boundary value problem refers to the forward model: the…
This paper develops a two-level fourth-order scheme for solving time-fractional convection-diffusion-reaction equation with variable coefficients subjected to suitable initial and boundary conditions. The basis properties of the new…
The functional distributions of particle trajectories have wide applications, including the occupation time in half-space, the first passage time, and the maximal displacement, etc. The models discussed in this paper are for characterizing…
A nontrivial conformally invariant model is obtained via generalization the method of obtaining conformally invariant models in $2D$ Euclidean space to the Euclidean space with dimension $D>2$. This method was previously developed by E.S.…
This paper is concerned with numerical solution of transport problems in heterogeneous porous media. A semi-discrete continuous-in-time formulation of the linear advection-diffusion equation is obtained by using a mixed hybrid finite…
We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary…
We carry out the enhanced group classification of a class of (1+1)-dimensional nonlinear diffusion-reaction equations with gradient-dependent diffusivity using the two-step version of the method of furcate splitting. For simultaneously…
We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…
This paper considers a time-fractional diffusion-wave equation with a high-contrast heterogeneous diffusion coefficient. A numerical solution to this problem can present great computational challenges due to its multiscale nature.…
In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. After time discretization, we utilize collocation technique and implement a product integration method in order to simplify the…
Equation of long-range particle drift and diffusion on three-dimensional physical lattice is suggested. This equation can be considered as a lattice analogof space-fractional Fokker-Planck equation for continuum. The lattice approach gives…
In this paper, we discuss the steady and time-dependent nonlinear convection-diffusion (advection-diffusion) equations with the Dirichlet boundary condition. For the steady nonlinear equation, we use an iteration method to reformulate the…
Invariant parameterization schemes for the eddy-vorticity flux in the barotropic vorticity equation on the beta-plane are constructed and then applied to turbulence modeling. This construction is realized by the exhaustive description of…
This article investigates the non-stationary reaction-diffusion-advection equation, emphasizing solutions with internal layers and the associated inverse problems. We examine a nonlinear singularly perturbed partial differential equation…
Numerical solutions of a non-Fickian diffusion equation belonging to a hyperbolic type are presented in one space dimension. The Brownian particle modelled by this diffusion equation is subjected to a symmetric periodic potential whose…
This paper focuses on a nonlinear convection-diffusion equation with space and time-fractional Laplacian operators of orders $1<\beta<2$ and $0<\alpha\leq1$, respectively. We develop local discontinuous Galerkin methods, including Legendre…
We discuss the derivation and the solutions of integro-differential equations (variable-order time-fractional diffusion equations) following as continuous limits for lattice continuous time random walk schemes with power-law waiting-time…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
A multiple exp-function method to exact multiple wave solutions of nonlinear partial differential equations is proposed. The method is oriented towards ease of use and capability of computer algebra systems, and provides a direct and…