High-order energy and linear momentum conserving methods for the Klein-Gordon equation

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Article number200
JournalMathematics
Volume6
Issue number10
DOIs
StatePublished - Oct 12 2018

Fingerprint

Klein-Gordon Equation
Momentum
High-order Methods
Numerical Methods
Higher Order
Numerical Scheme
Energy
Optimal Error Estimates
Superconvergence
Wave Function
Quantum Mechanics
Conservation
Verify
Numerical Examples
Model

Keywords

  • Energy-conserving method
  • High-order numerical methods
  • Linear momentum conservation
  • Local discontinuous Galerkin methods
  • Optimal error estimates
  • Superconvergence
  • The Klein-Gordon equation

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

High-order energy and linear momentum conserving methods for the Klein-Gordon equation. / Yang, He.

In: Mathematics, Vol. 6, No. 10, 200, 12.10.2018.

Research output: Contribution to journalArticle

@article{55c8e18ffa574e0e8a4d0c04143f9d9d,
title = "High-order energy and linear momentum conserving methods for the Klein-Gordon equation",
abstract = "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.",
keywords = "Energy-conserving method, High-order numerical methods, Linear momentum conservation, Local discontinuous Galerkin methods, Optimal error estimates, Superconvergence, The Klein-Gordon equation",
author = "He Yang",
year = "2018",
month = "10",
day = "12",
doi = "10.3390/math6100200",
language = "English (US)",
volume = "6",
journal = "Mathematics",
issn = "2227-7390",
publisher = "MDPI AG",
number = "10",

}

TY - JOUR

T1 - High-order energy and linear momentum conserving methods for the Klein-Gordon equation

AU - Yang, He

PY - 2018/10/12

Y1 - 2018/10/12

N2 - 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.

AB - 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.

KW - Energy-conserving method

KW - High-order numerical methods

KW - Linear momentum conservation

KW - Local discontinuous Galerkin methods

KW - Optimal error estimates

KW - Superconvergence

KW - The Klein-Gordon equation

UR - http://www.scopus.com/inward/record.url?scp=85054854114&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85054854114&partnerID=8YFLogxK

U2 - 10.3390/math6100200

DO - 10.3390/math6100200

M3 - Article

AN - SCOPUS:85054854114

VL - 6

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 10

M1 - 200

ER -