Numerical solution of a parabolic equation with non-local boundary specifications

2003 ◽  
Vol 145 (1) ◽  
pp. 185-194 ◽  
Author(s):  
Mehdi Dehghan
Keyword(s):  
Parabolic Equation ◽  
Numerical Solution ◽  
Local Boundary ◽  
Non Local

scholarly journals ERROR ANALYSIS OF LEGENDRE-GALERKIN SPECTRAL METHOD FOR A PARABOLIC EQUATION WITH DIRICHLET-TYPE NON-LOCAL BOUNDARY CONDITIONS

2021 ◽  
Vol 26 (2) ◽  
pp. 287-303
Author(s):  
Abdeldjalil Chattouh ◽  
Khaled Saoudi
Keyword(s):  
Parabolic Equation ◽  
Error Analysis ◽  
Boundary Conditions ◽  
Spectral Method ◽  
Time Derivative ◽  
Stability And Convergence ◽  
Local Boundary ◽  
Dirichlet Type ◽  
Non Local ◽  
Galerkin Spectral Method

An efficient Legendre-Galerkin spectral method and its error analysis for a one-dimensional parabolic equation with Dirichlet-type non-local boundary conditions are presented in this paper. The spatial discretization is based on Galerkin formulation and the Legendre orthogonal polynomials, while the time derivative is discretized by using the symmetric Euler finite difference schema. The stability and convergence of the semi-discrete spectral approximation are rigorously set up by following a novel approach to overcome difficulties caused by the non-locality of the boundary condition. Several numerical tests are included to confirm the efficacy of the proposed method and to support the theoretical results.

On the non-local boundary-value problem for a parabolic equation

1993 ◽  
Vol 54 (4) ◽  
pp. 1045-1057 ◽  
Author(s):  
L. A. Muravei ◽  
A. V. Filinovskii
Keyword(s):  
Parabolic Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Local Boundary ◽  
Non Local

ON A PARABOLIC EQUATION WITH NON-LOCAL BOUNDARY CONDITION

1993 ◽  
Vol 03 (06) ◽  
pp. 789-804
Author(s):  
ROBERTO GIANNI
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Existence And Uniqueness ◽  
Perfect Conductor ◽  
Uniqueness Theorems ◽  
Physical Situation ◽  
Local Boundary ◽  
Metallic Conductor ◽  
Local Boundary Condition ◽  
Non Local

Existence and uniqueness theorems are proved for a parabolic equation satisfying various kinds of non-local boundary conditions. Applications of these results are made to the physical situation in which a non-metallic conductor is in contact with a perfect conductor or with a well stirred fluid, and the conductor (or the fluid) is allowed to undergo a change of phase.

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