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In this paper, we obtained the sufficient conditions for the existence of solutions to the discrete boundary value problems of fractional difference equation depending on parameters. We use Krasnoselskii fixed point theorem to establish the…
We present an algorithm for the numerical solution of the equations governing combustion in porous inert media. The discretization of the flow problem is performed by the mixed finite element method, the transport problems are discretized…
We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…
In this paper, we develop regularized discrete least squares collocation and finite volume methods for solving two-dimensional nonlinear time-dependent partial differential equations on irregular domains. The solution is approximated using…
This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for…
When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…
This paper studies the existence of minimal solutions to two-point boundary value problems for quasi-monotone dynamical systems. Specifically, the pointwise infimum of all supersolutions is shown to coincide with the minimal solution. This…
A full multigrid finite element method is proposed for semilinear elliptic equations. The main idea is to transform the solution of the semilinear problem into a series of solutions of the corresponding linear boundary value problems on the…
In this work we propose a novel approach to investigate boundary value problems (BVPs) for fully third order differential equations. It is based on the reduction of BVPs to operator equations for the nonlinear terms but not for the…
Nonlinear systems of partial differential equations (PDEs) may permit several distinct solutions. The typical current approach to finding distinct solutions is to start Newton's method with many different initial guesses, hoping to find…
In this work we provide conditions for the existence of solutions to nonlinear boundary value problems of the form \begin{equation*} y(t+n)+a_{n-1}(t)y(t+n-1)+\cdots a_0(t)y(t)=g(t,y(t+m-1)) \end{equation*} subject to \begin{equation*}…
Existing theoretical stabilization results for linear, hyperbolic multi-dimensional problems are extended to the discretized multi-dimensional problems. In contrast to existing theoretical and numerical analysis in the spatially…
We propose a method for the treatment of two--point boundary value problems given by nonlinear ordinary differential equations. The approach leads to sequences of roots of Hankel determinants that converge rapidly towards the unknown…
A moving mesh finite difference method based on the moving mesh partial differential equation is proposed for the numerical solution of the 2T model for multi-material, non-equilibrium radiation diffusion equations. The model involves…
Boundary value problems in ODEs arise in modelling many physical situations from microscale to mega scale. Such two-point boundary value problems (BVPs) are complex and often possess no analytical closed form solutions. So, one has to rely…
This is a study of certain finite element methods designed for convection-dominated, time-dependent partial differential equations. Specifically, we analyze high order space-time tensor product finite element discretizations, used in a…
The existence of numerical solutions to a fourth order singular boundary value problem arising in the theory of epitaxial growth is studied. An iterative numerical method is applied on a second order nonlinear singular boundary value…
We investigate linear boundary value problems for first-order one-dimensional hyperbolic systems in a strip. We establish conditions for existence and uniqueness of bounded continuous solutions. For that we suppose that the non-diagonal…
The goal of this paper is to provide computational tools able to find a solution of a system of polynomial inequalities. The set of inequalities is reformulated as a system of polynomial equations. Three different methods, two of which…
Adomian decomposition method is used for solving the seventh order boundary value problems. The approximate solutions of the problems are calculated in the form of a rapid convergent series and not at grid points. Two numerical examples…