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

• Main Author: He Yang
• Format: Article
• Language: English
• Published: MDPI AG 2018-10-01
• Series: Mathematics
• Subjects: high-order numerical methods; the Klein-Gordon equation; energy-conserving method; linear momentum conservation; local discontinuous Galerkin methods; optimal error estimates; superconvergence
• Online Access: http://www.mdpi.com/2227-7390/6/10/200

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.