Finite Difference Methods for the Heat Equation with a Nonlocal Boundary Condition

2015 ◽  
Vol 33 (1) ◽  
pp. 17-32 ◽  
Author(s):  
V. Thomée and A.S. Vasudeva Murthy
Keyword(s):  
Boundary Condition ◽  
Finite Difference ◽  
Heat Equation ◽  
Nonlocal Boundary Condition ◽  
Finite Difference Methods ◽  
Nonlocal Boundary ◽  
Difference Methods

scholarly journals Rothe time-discretization method for the semilinear heat equation subject to a nonlocal boundary condition

2006 ◽  
Vol 2006 ◽  
pp. 1-20 ◽  
Author(s):  
Nabil Merazga ◽  
Abdelfatah Bouziani
Keyword(s):  
Boundary Condition ◽  
Heat Equation ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Time Discretization ◽  
Neumann Condition ◽  
Integral Boundary ◽  
Semilinear Heat Equation ◽  
Rothe Method ◽  
The Given

This paper is devoted to prove, in a nonclassical function space, the weak solvability of a mixed problem which combines a Neumann condition and an integral boundary condition for the semilinear one-dimensional heat equation. The investigation is made by means of approximation by the Rothe method which is based on a semidiscretization of the given problem with respect to the time variable.

scholarly journals Finite difference approximation of an elliptic problem with nonlocal boundary condition

Filomat ◽  
2016 ◽  
Vol 30 (6) ◽  
pp. 1549-1557
Author(s):  
Sandra Hodzic ◽  
Bosko Jovanovic
Keyword(s):  
Boundary Condition ◽  
Weak Solution ◽  
Finite Difference ◽  
Existence And Uniqueness ◽  
Input Data ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Sobolev Norm ◽  
Finite Difference Approximation ◽  
Difference Approximation

We consider Poisson?s equation on the unit square with a nonlocal boundary condition. The existence and uniqueness of its weak solution in Sobolev spaceH1 is proved. A finite difference scheme approximating this problem is proposed. An error estimate compatible with the smoothness of input data in discrete H1 Sobolev norm is obtained.

scholarly journals Investigation of complex eigenvalues for a stationary problem with two-point nonlocal boundary condition

2011 ◽  
Vol 52 ◽  
pp. 303-308
Author(s):  
Kristina Skučaitė-Bingelė ◽  
Artūras Štikonas
Keyword(s):  
Boundary Condition ◽  
Finite Difference ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Nonlocal Boundary Conditions ◽  
Stationary Problem ◽  
Finite Difference Schemes ◽  
Complex Eigenvalues ◽  
Sturm Liouville

The Sturm–Liouville problem with one classical and another two-point nonlocal boundary condition is considered in this paper. These problems with nonlocal boundary condition are not self-adjoint, so the spectrum has complex points. We investigate how the spectrum in the complex plane of these problems (and for the Finite-Difference Schemes) depends on parameters γ  and ξ  of the nonlocal boundary conditions.

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