83 research outputs found
Hypothesis on the Solvability of Parabolic Equations with nonlocal Condition
Numerous and different nonlocal conditions for the solvability of parabolic equations were researched in many articles and reports. The article presented analyzes such conditions imposed, and observes that the existence and uniqueness of the solution of parabolic equation is related mainly to ”smallness” of functions, involved in nonlocal conditions. As a consequence the hypothesis has been made, stating the assumptions on functions in nonlocal conditions are related to numerical algorithms of solving parabolic equations, and not to the parabolic equation itself
Numerical Analysis of the Eigenvalue Problem for One-Dimensional Differential Operator with Nonlocal Integral Conditions
In this paper the eigenvalue problem for one-dimensional differential operator with nonlocal integral conditions is investigated numerically. The special cases of general problem are analyzed and hypothesis about the dependence of the spectral structure of that problem on the coefficient of differential operator and the parameters of nonlocal conditions are formulated
On stability in the maximum norm of difference scheme for nonlinear parabolic equation with nonlocal condition
We construct and analyze the backward Euler method for one nonlinear one-dimensional parabolic equation with nonlocal boundary condition. The main objective of this article is to investigate the stability and convergence of the difference scheme in the maximum norm. For this purpose, we use the M-matrices theory. We describe some new approach for the estimation of the error of solution and construct the majorant for it. Some conclusions and discussion of our approach are presented
Numerical solution of nonlinear elliptic equation with nonlocal condition
Two iterative methods are considered for the system of difference equations approximating two-dimensional nonlinear elliptic equation with the nonlocal integral condition. Motivation and possible applications of the problem present in the paper coincide with the small volume problems in hydrodynamics. The differential problem considered in the article is some generalization of the boundary value problem for minimal surface equation
Alternating-direction method for a mildly nonlinear elliptic equation with nonlocal integral conditions
The present paper deals with a generalization of the alternating-direction implicit (ADI) method for the two-dimensional nonlinear Poisson equation in a rectangular domain with integral boundary condition in one coordinate direction. The analysis of results of computational experiments is presented
On iterative methods for some elliptic equations with nonlocal conditions
The iterative methods for the solution of the system of the difference equations derived from the elliptic equation with nonlocal conditions are considered. The case of the matrix of the difference equations system being the M-matrix is investigated. Main results for the convergence of the iterative methods are obtained considering the structure of the spectrum of the difference operators with nonlocal conditions. Furthermore, the case when the matrix of the system of difference equations has only positive eigenvalues was investigated. The survey of results on convergence of iterative methods for difference problem with nonlocal condition is also presented
On iterative methods for some elliptic equations with nonlocal conditions
The iterative methods for the solution of the system of the difference equations derived from the elliptic equation with nonlocal conditions are considered. The case of the matrix of the difference equations system being the M-matrix is investigated. Main results for the convergence of the iterative methods are obtained considering the structure of the spectrum of the difference operators with nonlocal conditions. Furthermore, the case when the matrix of the system of difference equations has only positive eigenvalues was investigated. The survey of results on convergence of iterative methods for difference problem with nonlocal condition is also presented.
1The research was partially supported by the Research Council of Lithuania (grant No. MIP-051/2011).
2The research was partially supported by the Research Council of Lithuania (grant No. MIP-047/2014)
On the stability of explicit finite difference schemes for a pseudoparabolic equation with nonlocal conditions
A new explicit conditionally consistent finite difference scheme for one-dimensional third-order linear pseudoparabolic equation with nonlocal conditions is constructed. The stability of the finite difference scheme is investigated by analysing a nonlinear eigenvalue problem. The stability conditions are stated and stability regions are described. Some numerical experiments are presented in order to validate theoretical results
Application of M-matrices theory to numerical investigation of a nonlinear elliptic equation with an integral condition
The iterative methods to solve the system of the difference equations derived from the nonlinear elliptic equation with integral condition are considered. The convergence of these methods is proved using the properties of M-matrices, in particular, the regular splitting of an M-matrix. To our knowledge, the theory of M-matrices has not ever been applied to convergence of iterative methods for system of nonlinear difference equations. The main results for the convergence of the iterative methods are obtained by considering the structure of the spectrum of the two-dimensional difference operators with integral condition.
*The research was partially supported by the Research Council of Lithuania (grant No. MIP-047/2014)
Modelling of wood drying and an influence of lumber geometry on drying dynamics
Modelling of wood drying is analyzed. Wood drying involves moisture transfer from the interior of the wood to the surface, then from the wood surface to the surrounding air. These processes can be characterized by the internal and surface moisture transfer coefficients. A model of the two-dimensional moisture transfer is suggested to determine these coefficients in contrast to the one-dimensional model which was proposed in [12]. The model is based on a diffusion equation with a variable diffusion coefficient. The insufficiency of the one-dimensional model is considered. The influence of the geometry of a lumber on determination of the surface emission and diffusion coefficients and on the dynamics of drying is investigated
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