Numerical solution of coupled nonlinear Klein-Gordon equations on unbounded domains
Yinong Tai1, Hongwei Li1, Zhaojie Zhou1
1School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, People's Republic of China.
Physical Review. E
|September 16, 2022
Summary
This study introduces an artificial boundary method for solving nonlinear Klein-Gordon equations on unbounded domains. The approach effectively handles nonlinearity and reduces the problem to a solvable form, verified by numerical examples.
Area of Science:
- Computational Physics
- Applied Mathematics
- Numerical Analysis
Background:
- Coupled nonlinear Klein-Gordon equations are fundamental in various physics fields.
- Solving these equations on unbounded domains presents significant numerical challenges.
- Existing methods often struggle with nonlinearity and domain extension.
Purpose of the Study:
- To develop an efficient numerical method for solving coupled nonlinear Klein-Gordon equations on unbounded domains.
- To introduce a unified approach for handling coupled nonlinearity.
- To validate the proposed method's accuracy and effectiveness.
Main Methods:
- Application of the artificial boundary method.
- Design of local artificial boundary conditions.
- Reduction to an initial boundary value problem on a bounded domain.
- Utilizing the finite difference method for efficient solution.
Main Results:
- Successfully transformed the unbounded domain problem into a bounded one.
- Demonstrated an effective way to overcome coupled nonlinearity.
- Numerical examples confirmed the method's accuracy and efficiency.
Conclusions:
- The artificial boundary method provides a robust framework for solving these complex equations.
- The proposed approach offers a computationally efficient and accurate solution.
- This method is applicable to a range of problems involving nonlinear wave phenomena.
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