Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 83, Issue 3, Pages -Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-020-01245-6
Keywords
Nonlinear wave equations; Unconditionally energy-conserving method; SAV; Arbitrarily high-order accuracy
Categories
Funding
- National Natural Science Foundation of China (NSFC) [11771162, 11971010]
- Research Grants Council of the Hong Kong Special Administrative Region, China [CityU 11302519]
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A key issue in developing efficient numerical schemes for nonlinear wave equations is the energy-conserving. Most existing schemes of the energy-conserving are fully implicit and the schemes require an extra iteration at each time step and considerable computational cost for a long time simulation, while the widely-usedq-stage (implicit) Gauss scheme (method) only preserves polynomial Hamiltonians up to degree 2q. In this paper, we present a family of linearly implicit and high-order energy-conserving schemes for solving nonlinear wave equations. The construction of schemes is based on recently-developed scalar auxiliary variable technique with a combination of classical high-order Gauss methods and extrapolation approximation. We prove that the proposed schemes are unconditionally energy-conserved for a general nonlinear wave equation. Numerical results are given to show the energy-conserving and the effectiveness of schemes.
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