Boundary Conditions for Time Dependent Problems with an Artificial Boundary.

1977 ◽  
Author(s):  
Bertil Gustafsson ◽  
Heinz-Otto Kreiss
Keyword(s):  
Boundary Conditions ◽  
Time Dependent ◽  
Artificial Boundary ◽  
Time Dependent Problems

scholarly journals Transparent Boundary Conditions for Time-Dependent Problems

2008 ◽  
Vol 30 (5) ◽  
pp. 2358-2385 ◽  
Author(s):  
Daniel Ruprecht ◽  
Achim Schädle ◽  
Frank Schmidt ◽  
Lin Zschiedrich
Keyword(s):  
Boundary Conditions ◽  
Time Dependent ◽  
Transparent Boundary Conditions ◽  
Time Dependent Problems

scholarly journals Derivation of boundary conditions for the artificial boundaries associated with the solution of certain time dependent problems by Lax–Wendroff type difference schemes

1982 ◽  
Vol 25 (1) ◽  
pp. 1-18 ◽  
Author(s):  
John C. Wilson
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Time Dependent ◽  
Finite Region ◽  
Partial Differential ◽  
Artificial Boundaries ◽  
Fixed Boundaries ◽  
Time Dependent Problems

Many problems involving the solution of partial differential equations require the solution over a finite region with fixed boundaries on which conditions are prescribed. It is a well known fact that the numerical solution of many such problems requires additional conditions on these boundaries and these conditions must be chosen to ensure stability. This problem has been considered by, amongst others, Kreiss [11, 12, 13], Osher [16, 17], Gustafsson et al. [9] Gottlieb and Tarkel [7] and Burns [1]

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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