Artificial boundary conditions for nonlinear time fractional Burgers’ equation on unbounded domains

2021 ◽  
pp. 107277
Author(s):  
Hongwei Li ◽  
Yuchen Wu
Keyword(s):  
Boundary Conditions ◽  
Burgers Equation ◽  
Unbounded Domains ◽  
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.

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