scholarly journals ON SOLVABILITY OF NONLOCAL PROBLEM FOR THIRD-ORDER EQUATION

2017 ◽  
Vol 23 (1) ◽  
pp. 15-20
Author(s):  
O. M. Ketchina
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Nonlocal Problem ◽  
Goursat Problem ◽  
Rectangular Domain ◽  
Integral Conditions ◽  
Third Order ◽  
Partial Differential ◽  
Integral Analogue ◽  
Equivalent Reduction

In this paper nonlocal problem with integral conditions for partial differential equation of the third order is considered. The existence of a unique classical solution is proved in rectangular domain. The proof is carried out by the method of auxiliary problems. At first the problem for a new function for partial differential equation of the first order is considered. Then the solvability of integral analogue of Goursat problem for hyperbolic equation of the second order is proved by equivalent reduction of the problem to the Volterra integral equation of the second kind.

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.

Adaptive Finite Element Method for Solving Poisson Partial Differential Equation

2021 ◽  
Vol 4 (1) ◽  
pp. 1-18
Author(s):  
Gokul KC ◽  
Ram Prasad Dulal
Keyword(s):  
Differential Equation ◽  
Finite Element Method ◽  
Partial Differential Equation ◽  
Finite Element ◽  
Poisson Equation ◽  
Rectangular Domain ◽  
Adaptive Finite Element Method ◽  
Adaptive Finite Element ◽  
Partial Differential ◽  
Element Method

Poisson equation is an elliptic partial differential equation, a generalization of Laplace equation. Finite element method is a widely used method for numerically solving partial differential equations. Adaptive finite element method distributes more mesh nodes around the area where singularity of the solution happens. In this paper, Poisson equation is solved using finite element method in a rectangular domain with Dirichlet and Neumann boundary conditions. Posteriori error analysis is used to mark the refinement area of the mesh. Dorfler adaptive algorithm is used to refine the marked mesh. The obtained results are compared with exact solutions and displayed graphically.

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