Fast Iterative Solution of Poisson Equation With Neumann Boundary Conditions In Nonorthogonal Curvilinear Coordinate Systems By A Multiple Grid Method

1983 ◽  
Vol 6 (1) ◽  
pp. 1-15
Author(s):  
H. Rieger ◽  
U. Projahn ◽  
H. Beer
Keyword(s):  
Boundary Conditions ◽  
Poisson Equation ◽  
Grid Method ◽  
Neumann Boundary ◽  
Iterative Solution ◽  
Neumann Boundary Conditions ◽  
Coordinate Systems ◽  
Curvilinear Coordinate

On the Treatment of Neumann Boundary Conditions in Solving Poisson Equation Using Meshless Galerkin Method

2013 ◽  
Vol 816-817 ◽  
pp. 734-738
Author(s):  
Xiang Dong Zhang ◽  
Lei Wang
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Poisson Equation ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Proper Method ◽  
Meshless Galerkin Method

This paper studies the treatment of Neumann boundary conditions when solving Poisson equation using meshless Galerkin method. We find that Neumann boundary conditions can be implemented more accurately by adopting proper method. Advantages of doing this are also shown.

scholarly journals Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 1552-1564
Author(s):  
Huimin Tian ◽  
Lingling Zhang
Keyword(s):  
Boundary Conditions ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Nonlocal Reaction

Abstract In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u ( x , t ) u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.

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