High-order local artificial boundary conditions for problems in unbounded domains

2000 ◽  
Vol 188 (1-3) ◽  
pp. 455-471 ◽  
Author(s):  
Weizhu Bao ◽  
Houde Han
Keyword(s):  
Boundary Conditions ◽  
Unbounded Domains ◽  
High Order ◽  
Artificial Boundary ◽  
Artificial Boundary Conditions

A FDM for Burgers’ Equation on Unbounded Domains Using High-Order Artificial Boundary Conditions

2017 ◽  
Vol 865 ◽  
pp. 233-238
Author(s):  
Quan Zheng ◽  
Yu Feng Liu
Keyword(s):  
Boundary Conditions ◽  
Heat Equation ◽  
Unbounded Domain ◽  
Burgers Equation ◽  
High Order ◽  
Computational Domain ◽  
Artificial Boundary ◽  
Artificial Boundary Conditions ◽  
Second Order Convergence ◽  
The Stability

Burgers’ equation on an unbounded domain is an important mathematical model to treat with some external problems of fluid materials. In this paper, we study a FDM of Burgers’ equation using high-order artificial boundary conditions on the unbounded domain. First, the original problem is converted into the heat equation on an unbounded domain by Hopf-Cole transformation. Thus the difficulty of nonlinearity of Burgers’ equation is overcome. Second, high-order artificial boundary conditions are given by using Padé approximation and Laplace transformation. And the conditions confine the heat equation onto a bounded computational domain. Third, we prove the solutions of the resulting heat equation and Burgers’ equation are both stable. Fourth, we establish the FDM for Burgers’ equation on the bounded computational domain. Finally, a numerical example demonstrates the stability, the effectiveness and the second-order convergence of the proposed method.

Artificial Boundary Conditions for Nonlocal Heat Equations on Unbounded Domain

2016 ◽  
Vol 21 (1) ◽  
pp. 16-39 ◽  
Author(s):  
Wei Zhang ◽  
Jiang Yang ◽  
Jiwei Zhang ◽  
Qiang Du
Keyword(s):  
Boundary Conditions ◽  
Initial Boundary ◽  
High Order ◽  
Memory Storage ◽  
Heat Equations ◽  
Infinite Domain ◽  
Artificial Boundary ◽  
Artificial Boundary Conditions ◽  
Fully Discrete ◽  
Initial Boundary Value

AbstractThis paper is concerned with numerical approximations of a nonlocal heat equation define on an infinite domain. Two classes of artificial boundary conditions (ABCs) are designed, namely, nonlocal analog Dirichlet-to-Neumann-type ABCs (global in time) and high-order Padé approximate ABCs (local in time). These ABCs reformulate the original problem into an initial-boundary-value (IBV) problem on a bounded domain. For the global ABCs, we adopt a fast evolution to enhance computational efficiency and reduce memory storage. High order fully discrete schemes, both second-order in time and space, are given to discretize two reduced problems. Extensive numerical experiments are carried out to show the accuracy and efficiency of the proposed methods.

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