scholarly journals Time exponential splitting technique for the Klein–Gordon equation with Hagstrom–Warburton high-order absorbing boundary conditions

2016 ◽  
Vol 311 ◽  
pp. 196-212 ◽  
Author(s):  
I. Alonso-Mallo ◽  
A.M. Portillo
Keyword(s):  
Boundary Conditions ◽  
Gordon Equation ◽  
Absorbing Boundary Conditions ◽  
High Order ◽  
Absorbing Boundary ◽  
Splitting Technique ◽  
Klein Gordon ◽  
Exponential Splitting ◽  
Klein Gordon Equation

High order local absorbing boundary conditions for acoustic and elastic scattering

2020 ◽  
Vol 148 (4) ◽  
pp. 2451-2451
Author(s):  
Vianey Villamizar ◽  
Tahsin Khajah ◽  
Sebastian Acosta ◽  
Dane Grundvig ◽  
Jacob Badger ◽  
...  
Keyword(s):  
Elastic Scattering ◽  
Boundary Conditions ◽  
Absorbing Boundary Conditions ◽  
High Order ◽  
Absorbing Boundary

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.

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