Related papers: Structure-preserving finite difference schemes for…
In this work, we develop novel structure-preserving numerical schemes for a class of nonlinear Fokker--Planck equations with nonlocal interactions. Such equations can cover many cases of importance, such as porous medium equations with…
The present paper is a numerical study of the dynamics of solitary wave solutions of the fractional nonlinear Schr\"{o}dinger equation, whose existence was analyzed by the authors in the first part of the project. The computational study…
We construct a finite element like scheme for fully non-linear integro-partial differential equations arising in optimal control of jump-processes. Special cases of these equations include optimal portfolio and option pricing equations in…
Invariant finite-difference schemes for the one-dimensional shallow water equations in the presence of a magnetic field for various bottom topographies are constructed. Based on the results of the group classification recently carried out…
We discuss structure-preserving numerical discretizations for repulsive and attractive Euler-Poisson equations that find applications in fluid-plasma and self-gravitation modeling. The scheme is fully discrete and structure preserving in…
Large-scale simulations of the wave equation in electromagnetism, seismology, and acoustics, can be solved efficiently by finite difference methods. The accuracy of these numerical solutions usually depends on the minimization of…
Difference schemes for the time-fractional diffusion equation with variable coefficients and nonlocal boundary conditions containing real parameters $\alpha$ and $\beta$ are considered. By the method of energy inequalities, for the solution…
The numerical solution of a nonlinear and space-fractional anti-diffusive equation used to model dune morphodynamics is considered. Spatial discretization is effected using a finite element method whereas the Crank-Nicolson scheme is used…
We evaluate the influence of local resolution, eddy viscosity, coastline structure, and boundary conditions on the numerical representation of boundary currents in a finite element shallow-water model. The use of finite element…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
We propose a new numerical approach to compute nonclassical solutions to hyperbolic conservation laws. The class of finite difference schemes presented here is fully conservative and keep nonclassical shock waves as sharp interfaces,…
A nonlinear divergence parabolic equation with dynamic boundary conditions of Wentzell type is studied. The existence and uniqueness of a strong solution is obtained as the limit of a finite difference scheme, in the time dependent case and…
This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…
In this paper we present a numerical scheme for nonlinear continuity equations, which is based on the gradient flow formulation of an energy functional with respect to the quadratic transportation distance. It can be applied to a large…
This paper investigates the structure preservation and convergence analysis of a class of fully discrete finite difference schemes for the stochastic heat equation driven by L\'evy space-time white noise. The novelty lies in the…
Using the method of equivariant moving frames, we present a procedure for constructing symmetry-preserving finite element methods for second-order ordinary differential equations. Using the method of lines, we then indicate how our…
In this paper, we investigate the lifespan estimates of classical solutions of the initial value problems for semilinear wave equations of derivative type with characteristic weights in one space dimension. Such equations provide us basic…
This paper introduces improved numerical techniques for addressing numerical boundary and interface coupling conditions in the context of diffusion equations in cellular biophysics or heat conduction problems in fluid-structure…
We study a family of structure-preserving deterministic numerical schemes for Lindblad equations. This family of schemes has a simple form and can systemically achieve arbitrary high-order accuracy in theory. Moreover, these schemes can…
By the simple finite element method, we study the symplectic, multisymplectic structures and relevant preserving properties in some semi-linear elliptic boundary value problem in one-dimensional and two-dimensional spaces respectively. We…