Applicability of the sweep method to the difference analog of a De la Valee-Poussin boundary value problem

1969 ◽  
Vol 9 (2) ◽  
pp. 276-284
Author(s):  
A.L. Teptin
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Sweep Method ◽  
Difference Analog ◽  
The Difference

scholarly journals On Third Order Stable Difference Scheme for Hyperbolic Multipoint Nonlocal Boundary Value Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Ozgur Yildirim ◽  
Meltem Uzun
Keyword(s):  
Boundary Value Problem ◽  
Difference Scheme ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Stability Estimates ◽  
Nonlocal Boundary Value Problem ◽  
Third Order ◽  
Order Of Accuracy ◽  
Definite Operator ◽  
The Difference

This paper presents a third order of accuracy stable difference scheme for the approximate solution of multipoint nonlocal boundary value problem of the hyperbolic type in a Hilbert space with self-adjoint positive definite operator. Stability estimates for solution of the difference scheme are obtained. Some results of numerical experiments that support theoretical statements are presented.

scholarly journals Global theorem of existence and uniqueness of the firstboundary value problem for nonlinear integrodifferential equations ofparabolic type

2017 ◽  
Vol 21 (3) ◽  
pp. 64-72
Author(s):  
O.P. Filatov
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Parabolic Type ◽  
Current Application ◽  
Real Model ◽  
Fuel Tanks ◽  
The Difference ◽  
The Right ◽  
A Current

Global theorem of existence and uniqueness of solution of the first boundary value problem for nonlinear integrodifferential equation of parabolic type is proved. If the right-hand side of the equation is integrally bounded, then we have estimate of the norm of the difference of two solutions, which implies continuous dependence of solution on the initial function and uniqueness of so- lution of the first boundary value problem. The problem under consideration generalizes the real model for measuring the level of incompressible fluid in the fuel tanks missiles. Therefore, such problem have a current application.

A High-Order Difference Scheme for a Nonlocal Boundary-Value Problem for the Heat Equation

2001 ◽  
Vol 1 (4) ◽  
pp. 398-414 ◽  
Author(s):  
Zhi-Zhong Sun
Keyword(s):  
Boundary Value Problem ◽  
Difference Scheme ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
High Order ◽  
Order Difference ◽  
Local Boundary ◽  
Non Local ◽  
The Difference ◽  
Boundary Equations

Abstract This paper is concerned with a high order difference scheme for a non- local boundary-value problem of parabolic equation. The integrals in the boundary equations are approximated by the composite Simpson rule. The unconditional solv- ability and L_∞ convergence of the difference scheme is proved by the energy method. The convergence rate of the difference scheme is second order in time and fourth order in space. Some numerical examples are provided to illustrate the convergence.

scholarly journals An iteration method for the determination of an unknown boundary condition in a parabolic initial-boundary value problem

1989 ◽  
Vol 32 (1) ◽  
pp. 59-71 ◽  
Author(s):  
Michael Pilant ◽  
William Rundell
Keyword(s):  
Boundary Value Problem ◽  
Heat Conduction Problem ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Fourth Power ◽  
Unknown Boundary ◽  
The Difference ◽  
Image Position ◽  
Initial Boundary Value

Consider the initial boundary value problemIn the context of the heat conduction problem, this models the case where the heat flux across the ends at the rod is a function of the temperature. If the heat exchange between the rod and its surroundings is purely by convection, then one commonly assumes that f is a linear function of the difference in temperatures between the ends of the rod and that of the surroundings, (Newton's law of cooling). For the case of purely radiative transfer of energy a fourth power law for the function f is usual, (Stefan's law).

scholarly journals On the estimates of eigenvalues of the boundary value problem with large parameter

2015 ◽  
Vol 63 (1) ◽  
pp. 101-113 ◽  
Author(s):  
Alexey V. Filinovskiy
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Value Problem ◽  
Bounded Domain ◽  
Laplace Operator ◽  
Boundary Value ◽  
Dirichlet Condition ◽  
Large Parameter ◽  
Robin Condition ◽  
The Difference ◽  
The Laplace Operator

Abstract We consider the eigenvalue problem Δu + λu = 0 in Ω with Robin condition + αu = 0 on ∂Ω , where Ω ⊂ Rn , n ≥ 2 is a bounded domain and α is a real parameter. We obtain the estimates to the difference between λDk - λk(α) eigenvalue of the Laplace operator in with Dirichlet condition and the corresponding Robin eigenvalue for large positive values of for all k = 1,2,… We also show sharpness of these estimates in the power of α.

scholarly journals A fixed-point approach for decaying solutions of difference equations

2021 ◽  
Vol 379 (2191) ◽  
pp. 20190374
Author(s):  
Zuzana Došlá ◽  
Mauro Marini ◽  
Serena Matucci
Keyword(s):  
Fixed Point ◽  
Difference Equation ◽  
Boundary Value Problem ◽  
Difference Equations ◽  
Boundary Value ◽  
Future Research ◽  
Deviating Argument ◽  
Advanced Argument ◽  
Intermediate Solution ◽  
The Difference

A boundary value problem associated with the difference equation with advanced argument * Δ ( a n Φ ( Δ x n ) ) + b n Φ ( x n + p ) = 0 , n ≥ 1 is presented, where Φ ( u ) = | u | α sgn u , α  > 0, p is a positive integer and the sequences a , b , are positive. We deal with a particular type of decaying solution of (*), that is the so-called intermediate solution (see below for the definition). In particular, we prove the existence of this type of solution for (*) by reducing it to a suitable boundary value problem associated with a difference equation without deviating argument. Our approach is based on a fixed-point result for difference equations, which originates from existing ones stated in the continuous case. Some examples and suggestions for future research complete the paper. This article is part of the theme issue ‘Topological degree and fixed point theories in differential and difference equations’.

scholarly journals Study of a Numerical Method for Solving a Boundary Value Problem for a Differential Equation with a Fractional Time Derivative

2020 ◽  
pp. 64-69
Author(s):  
N.B Alimbekova ◽  
D.R. Baigereyev ◽  
M.N. Madiyarov
Keyword(s):  
Boundary Value Problem ◽  
Difference Scheme ◽  
A Priori Estimates ◽  
Boundary Value ◽  
Time Derivative ◽  
Smooth Functions ◽  
Differential Problem ◽  
Difference Problem ◽  
The Difference ◽  
Fractional Time Derivative

Recently, there has been an increased interest in the problem of numerical implementation of multiphase filtration models due to its enormous economic importance in the oil industry, hydrology, and nuclear waste management. In contrast to the classical models of filtration, filtration models in highly porous fractured formations with the fractal geometry of wells are not fully understood. The solution to this problem reduces to solving a system of differential equations with fractional derivatives. In the paper, a finite-difference scheme is constructed for solving the initial-boundary value problem for the convection-diffusion equation with a fractional time derivative in the sense of Caputo-Fabrizio. A priori estimates are obtained for solving a difference problem under the assumption that there is a solution to the problem in the class of sufficiently smooth functions that prove the uniqueness of the solution and the stability of the difference scheme. The convergence of the solution of the difference problem to the solution of the original differential problem with the second order in time and space variables is shown. The results of computational experiments confirming the reliability of theoretical analysis are presented.

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