Automatic GrabCut based lung extraction from endoscopic images with an initial boundary

AbstractA general class of implicit difference methods for nonlinear parabolic functional differential equations with initial boundary conditions of the Neumann type is constructed. Convergence results are proved by means of consistency and stability arguments. It is assumed that given functions satisfy nonlinear estimates of Perron type with respect to functional variables. Differential equations with deviated variables and differential integral problems can be obtained from a general model by specializing given operators. The results are illustrated by numerical examples.

Download Full-text

Convergence of Finite Fifference Method for Parabolic Problem

Computational Methods in Applied Mathematics ◽

10.2478/cmam-2003-0005 ◽

2003 ◽

Vol 3 (1) ◽

pp. 45-58 ◽

Cited By ~ 2

Author(s):

Dejan Bojović

Keyword(s):

Convergence Rate ◽

Boundary Value Problem ◽

Heat Equation ◽

Parabolic Problem ◽

Initial Boundary ◽

Initial Boundary Value Problem ◽

Variable Coefficients ◽

Rate Estimate ◽

Convergence Rate Estimate ◽

Initial Boundary Value

Abstract In this paper we consider the first initial boundary-value problem for the heat equation with variable coefficients in a domain (0; 1)x(0; 1)x(0; T]. We assume that the solution of the problem and the coefficients of the equation belong to the corresponding anisotropic Sobolev spaces. Convergence rate estimate which is consistent with the smoothness of the data is obtained.

Download Full-text

ON THE SOLVABILITY OF A MIXED PROBLEM WITH DEGREE LAPLACE OPERATORS WITH NONLOCAL BOUNDARY CONDITIONS

RSUH/RGGU Bulletin. Series Information Science. Information Security. Mathematics ◽

10.28995/2686-679x-2020-2-85-104 ◽

2020 ◽

pp. 85-104

Author(s):

Shakirbai G. Kasimov ◽

◽

Mahkambek M. Babaev ◽

◽

Keyword(s):

Boundary Conditions ◽

Spectral Problem ◽

Nonlocal Boundary ◽

Initial Boundary ◽

Initial Boundary Value Problem ◽

Nonlocal Boundary Conditions ◽

Laplace Operators ◽

Initial Boundary Problem ◽

Initial Boundary Value ◽

Delayed Time

The paper studies a problem with initial functions and boundary conditions for partial differential partial equations of fractional order in partial derivatives with a delayed time argument, with degree Laplace operators with spatial variables and nonlocal boundary conditions in Sobolev classes. The solution of the initial boundary-value problem is constructed as the series’ sum in the eigenfunction system of the multidimensional spectral problem. The eigenvalues are found for the spectral problem and the corresponding system of eigenfunctions is constructed. It is shown that the system of eigenfunctions is complete and forms a Riesz basis in the Sobolev subspace. Based on the completeness of the eigenfunctions system the uniqueness theorem for solving the problem is proved. In the Sobolev subspaces the existence of a regular solution to the stated initial-boundary problem is proved.

Download Full-text