Related papers: Flux-splitting schemes for parabolic problems
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…
Mathematical modeling of many physical processes such as diffusion, viscosity of fluids and combustion involves differential equations with small coefficients of higher derivatives. These may be small diffusion coefficients for modeling the…
In this study, we investigate a mixed problem linked to a second-order parabolic equation, characterized by temporal dependencies and variable~coefficients, and constrained by non-local, non-self-adjoint boundary conditions. By defining…
We consider a two-asset non-linear model of option pricing in an environment where the correlation is not known precisely, but varies between two known values. First we discuss the non-negativity of the solution of the equation. Next, we…
In this work, we consider the dynamic unsplittable flow problem. This variation of the unsplittable flow problem has received little attention so far. The unsplittable flow problem is an NP-hard extension of the multi-commodity flow problem…
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 this paper we are concerned with the initial boundary value problems of linear and semi-linear parabolic equations with mixed boundary conditions on non-cylindrical domains in spatial-temporal space. We obtain the existence of a weak…
Various classes of stable finite difference schemes can be constructed to obtain a numerical solution. It is important to select among all stable schemes such a scheme that is optimal in terms of certain additional criteria. In this study,…
We consider a boundary value problem for the parabolic Lam\'e type operator being a linearization of the Navier-Stokes' equations for compressible flow of Newtonian fluids. It consists of recovering a vector-function, satisfying the…
In this paper, we consider a class of initial-boundary value problems governed by pseudo-parabolic total variation flows. The principal characteristic of our problem lies in the velocity term of the diffusion flux, a feature that can bring…
The problem of choice of boundary conditions are discussed for the case of numerical integration of the shallow water equations on a substantially irregular relief. In modeling of unsteady surface water flows has a dynamic boundary…
This paper describes a class of scheme named "residual distribution schemes" or "fluctuation splitting schemes". They are a generalization of Roe's numerical flux in fluctuation form. The so-called multidimensional fluctuation schemes have…
In this article, we have developed a higher order compact numerical method for variable coefficient parabolic problems with mixed derivatives. The finite difference scheme, presented here for two-dimensional domains, is based on fourth…
We establish $L_{q,p}$-estimates and solvability for mixed Dirichlet-conormal problems for parabolic equations in a cylindrical Reifenberg-flat domain with a rough time-dependent separation.
This work deals with the problem of choosing a time step for the numerical solution of boundary value problems for parabolic equations. The problem solution is derived using the fully implicit scheme, whereas a time step is selected via…
We present a reformulation of unsteady turbulent flow simulations. The initial condition is relaxed and information is allowed to propagate both forward and backward in time. Simulations of chaotic dynamical systems with this reformulation…
Degenerate abstract parabolic equations with variable coefficients are studied. Here the boundary conditions are nonlocal. The maximal regularity properties of solutions for elliptic and parabolic problems and Strichartz type estimates in…
We consider an inverse boundary value problem for diffusion equations with multiple fractional time derivatives. We prove the uniqueness in determining a number of fractional time-derivative terms, the orders of the derivatives and…
An equation containing a fractional power of an elliptic operator of second order is studied for Dirichlet boundary conditions. Finite difference approximations in space are employed. The proposed numerical algorithm is based on solving an…
In this work we investigate a boundary problem with non-local conditions for mixed parabolic-hyperbolic type equation with three lines of type-changing with Caputo fractional derivative in the parabolic part. We equivalently reduce…