Numerical algorithm for the third-order partial differential equation with nonlocal boundary conditions

2017 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Kheireddine Belakroum ◽  
Assia Guezane-Lakoud
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Conditions ◽  
Numerical Algorithm ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Order Partial Differential Equation ◽  
Third Order ◽  
Partial Differential ◽  
The Third

scholarly journals A note on the nonlocal boundary value problem for a third order partial differential equation

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 801-808 ◽  
Author(s):  
Kh. Belakroum ◽  
A. Ashyralyev ◽  
A. Guezane-Lakoud
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Stability Estimates ◽  
Order Partial Differential Equation ◽  
Nonlocal Boundary Value Problem ◽  
Third Order ◽  
Partial Differential

The nonlocal boundary-value problem for a third order partial differential equation in a Hilbert space with a self-adjoint positive definite operator is considered. Applying operator approach, the theorem on stability for solution of this nonlocal boundary value problem is established. In applications, the stability estimates for the solution of three nonlocal boundary value problems for third order partial differential equations are obtained.

scholarly journals On the Solvability of a Mixed Problem for a High-Order Partial Differential Equation with Fractional Derivatives with Respect to Time, with Laplace Operators with Spatial Variables and Nonlocal Boundary Conditions in Sobolev Classes

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 235 ◽  
Author(s):  
Onur İlhan ◽  
Shakirbay Kasimov ◽  
Shonazar Otaev ◽  
Haci Baskonus
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Conditions ◽  
Mixed Problem ◽  
Fractional Derivatives ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Order Partial Differential Equation ◽  
Sobolev Classes ◽  
Spatial Variables

In this paper, we study the solvability of a mixed problem for a high-order partial differential equation with fractional derivatives with respect to time, and with Laplace operators with spatial variables and nonlocal boundary conditions in Sobolev classes.

scholarly journals A Stable Difference Scheme for a Third-Order Partial Differential Equation

2018 ◽  
Vol 64 (1) ◽  
pp. 1-19 ◽  
Author(s):  
A Ashyralyev ◽  
Kh Belakroum
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Approximate Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Difference Scheme ◽  
Nonlocal Boundary ◽  
Order Partial Differential Equation ◽  
Third Order ◽  
Partial Differential

The nonlocal boundary-value problem for a third order partial differential equation in a Hilbert space H with a self-adjoint positive definite operator A is considered. A stable three-step difference scheme for the approximate solution of the problem is presented. The main theorem on stability of this difference scheme is established. In applications, the stability estimates for the solution of difference schemes of the approximate solution of three nonlocal boundary value problems for third order partial differential equations are obtained. Numerical results for oneand two-dimensional third order partial differential equations are provided.

scholarly journals Mixed problem with nonlocal boundary conditions for a third-order partial differential equation of mixed type

2001 ◽  
Vol 26 (7) ◽  
pp. 417-426 ◽  
Author(s):  
M. Denche ◽  
A. L. Marhoune
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Conditions ◽  
Mixed Problem ◽  
Mixed Type ◽  
Order Partial Differential Equation ◽  
Third Order ◽  
Partial Differential ◽  
Integral Boundary ◽  
Equation Of Mixed Type

We study a mixed problem with integral boundary conditions for a third-order partial differential equation of mixed type. We prove the existence and uniqueness of the solution. The proof is based on two-sided a priori estimates and on the density of the range of the operator generated by the considered problem.

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