scholarly journals STRICTLY CONVERGENT ALGORITHM FOR AN ELLIPTIC EQUATION WITH NONLOCAL AND NONLINEAR BOUNDARY CONDITIONS

2012 ◽  
Vol 17 (1) ◽  
pp. 128-139 ◽  
Author(s):  
Karlis Birgelis ◽  
Uldis Raitums
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Radiative Heat ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Nonlinear Boundary Conditions ◽  
Local Boundary ◽  
Transfer Processes ◽  
Nonlocal Terms ◽  
Convergent Algorithm

The paper describes a formally strictly convergent algorithm for solving a class of elliptic problems with nonlinear and nonlocal boundary conditions, which arise in modeling of the steady-state conductive-radiative heat transfer processes. The proposed algorithm has two levels of iterations, where inner iterations by means of the damped Newton method solve an appropriate elliptic problem with nonlinear, but local boundary conditions, and outer iterations deal with nonlocal terms in boundary conditions.

scholarly journals Nonlocal systems of BVPS with asymptotically sublinear boundary conditions

2012 ◽  
Vol 6 (2) ◽  
pp. 174-193 ◽  
Author(s):  
Christopher Goodrich
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Coupled System ◽  
Nonlinear Boundary Conditions ◽  
Borel Measures ◽  
Boundary Functions ◽  
Nonlocal Terms ◽  
Nonlocal Nonlinear

In this paper we consider a coupled system of second-order boundary value problems with nonlocal, nonlinear boundary conditions. By imposing only a condition of asymptotic sublinear growth on the nonlinear boundary functions, we are able to achieve generalizations over existing works and, in particular, we allow for the nonlocal terms to be able to be represented as Lebesgue-Stieltjes integrals possessing signed Borel measures. Because we only suppose the sublinearity of the nonlinear boundary functions at positive infinity, we also remove many of the restrictive growth assumptions found in other recent works on closely related problems. We conclude with a numerical example to explicate the consequences of our main result.

scholarly journals Existence and uniqueness of nonlocal boundary conditions for Hilfer–Hadamard-type fractional differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ahmad Y. A. Salamooni ◽  
D. D. Pawar
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Nonlinear Boundary Conditions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential

AbstractIn this paper, we use some fixed point theorems in Banach space for studying the existence and uniqueness results for Hilfer–Hadamard-type fractional differential equations $$ {}_{\mathrm{H}}D^{\alpha ,\beta }x(t)+f\bigl(t,x(t)\bigr)=0 $$ D α , β H x ( t ) + f ( t , x ( t ) ) = 0 on the interval $(1,e]$ ( 1 , e ] with nonlinear boundary conditions $$ x(1+\epsilon )=\sum_{i=1}^{n-2}\nu _{i}x(\zeta _{i}),\qquad {}_{\mathrm{H}}D^{1,1}x(e)= \sum_{i=1}^{n-2} \sigma _{i}\, {}_{\mathrm{H}}D^{1,1}x( \zeta _{i}). $$ x ( 1 + ϵ ) = ∑ i = 1 n − 2 ν i x ( ζ i ) , H D 1 , 1 x ( e ) = ∑ i = 1 n − 2 σ i H D 1 , 1 x ( ζ i ) .

scholarly journals Nonlocal Boundary Conditions Are Applied to the Analysis of Curve Equations

2022 ◽  
Vol 16 ◽  
pp. 248-256
Author(s):  
Qingling Wang ◽  
Lingling Fang
Keyword(s):  
Boundary Conditions ◽  
Traditional Method ◽  
Solution Method ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Complex Curve ◽  
Equation Solution ◽  
Local Boundary ◽  
Non Local ◽  
Curve Equation

The traditional curve equation solution method has a low accuracy, so the non-local boundary conditions are applied to the curve equation solution. Firstly, the solution coordinate system is established, and then the key parameters are determined to solve the curve equation. Finally, the curve equation is solved by combining the non-local boundary conditions. The experiment proves that the method of this design is more accurate than the traditional method in solving simple curve equation or complex curve equation.

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

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.

Ordinary Differential Equations with Nonlinear Boundary Conditions

2002 ◽  
Vol 9 (2) ◽  
pp. 287-294
Author(s):  
Tadeusz Jankowski
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Existence Results ◽  
Monotone Iterative Technique ◽  
Lower And Upper Solutions ◽  
Iterative Technique ◽  
Monotone Iterative

Abstract The method of lower and upper solutions combined with the monotone iterative technique is used for ordinary differential equations with nonlinear boundary conditions. Some existence results are formulated for such problems.

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