Non-local boundary conditions for high-order parabolic equation algorithms

Wave Motion ◽  
2000 ◽  
Vol 31 (2) ◽  
pp. 117-129 ◽  
Author(s):  
Gary H. Brooke ◽  
David J. Thomson
Keyword(s):  
Parabolic Equation ◽  
Boundary Conditions ◽  
High Order ◽  
Local Boundary ◽  
Order Parabolic Equation ◽  
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.

Elliptic problem involving non-local boundary conditions

2019 ◽  
Vol 181 ◽  
pp. 87-100
Author(s):  
Noureddine Igbida ◽  
Soma Safimba
Keyword(s):  
Boundary Conditions ◽  
Elliptic Problem ◽  
Local Boundary ◽  
Non Local
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