Time-Dependent Singular Boundary Method for Scalar Wave Equation

2021 ◽  
pp. 109-120
Author(s):  
Jun-Pu Li ◽  
Qing-Hua Qin
Keyword(s):  
Wave Equation ◽  
Time Dependent ◽  
Singular Boundary ◽  
Scalar Wave ◽  
Scalar Wave Equation ◽  
Boundary Method ◽  
Singular Boundary Method

scholarly journals Meshless Singular Boundary Method for Nonlinear Sine-Gordon Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Yun Ji
Keyword(s):  
Gordon Equation ◽  
Neumann Boundary ◽  
Numerical Results ◽  
Time Dependent ◽  
Singular Boundary ◽  
Algebraic Equations ◽  
Sine Gordon Equation ◽  
Boundary Method ◽  
Singular Boundary Method ◽  
Good Agreement

A meshless method based on the singular boundary method is developed for the numerical solution of the time-dependent nonlinear sine-Gordon equation with Neumann boundary condition. In this method, by using a time discrete scheme to approximate the time derivatives, the time-dependent nonlinear problem is transformed into a sequence of time-independent linear boundary value problems. Then, the singular boundary method is used to establish the system of discrete algebraic equations. The present method is meshless, integration-free, and easy to implement. Numerical examples involving line and ring solitons are given to show the performance and efficiency of the proposed method. The numerical results are found to be in good agreement with the analytical solutions and the numerical results that exist in literature.

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