High-order multi-symplectic schemes for the nonlinear Klein–Gordon equation

2005 ◽  
Vol 166 (3) ◽  
pp. 608-632 ◽  
Author(s):  
Yushun Wang ◽  
Bin Wang
Keyword(s):  
Gordon Equation ◽  
High Order ◽  
Klein Gordon ◽  
Symplectic Schemes ◽  
Klein Gordon Equation

scholarly journals High-Order Energy and Linear Momentum Conserving Methods for the Klein-Gordon Equation

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 200 ◽  
Author(s):  
He Yang
Keyword(s):  
Numerical Methods ◽  
Gordon Equation ◽  
Free Particle ◽  
High Order ◽  
Linear Momentum ◽  
Relativistic Quantum Mechanics ◽  
Optimal Error Estimates ◽  
Numerical Schemes ◽  
Klein Gordon ◽  
Klein Gordon Equation

The Klein-Gordon equation is a model for free particle wave function in relativistic quantum mechanics. Many numerical methods have been proposed to solve the Klein-Gordon equation. However, efficient high-order numerical methods that preserve energy and linear momentum of the equation have not been considered. In this paper, we propose high-order numerical methods to solve the Klein-Gordon equation, present the energy and linear momentum conservation properties of our numerical schemes, and show the optimal error estimates and superconvergence property. We also verify the performance of our numerical schemes by some numerical examples.

Based on the Homotopy Analysis Method to Solve the Klein - Gordon Equation

2013 ◽  
Vol 278-280 ◽  
pp. 62-67
Author(s):  
Hai Yang Li ◽  
Ting Ting Wang ◽  
Xi Qin He
Keyword(s):  
Homotopy Analysis Method ◽  
Gordon Equation ◽  
Zero Order ◽  
High Order ◽  
Analysis Method ◽  
Deformation Equation ◽  
Order Deformation ◽  
Homotopy Analysis ◽  
Klein Gordon ◽  
Klein Gordon Equation

This paper applies the homotopy analysis method to solve Klein-Gordon equation, Firstly, structure a zero-order deformation equation. Then get the formal approximation of the model from high-order deformation equation and prove the effectiveness of the solution in the end.

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