An Efficient Energy-Preserving Numerical Algorithm for Nonlinear Wave Equations

XIE Jianqiang; WANG Can

doi:10.21656/1000-0887.460090

Volume 47 Issue 1

Jan. 2026

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XIE Jianqiang, WANG Can. An Efficient Energy-Preserving Numerical Algorithm for Nonlinear Wave Equations[J]. Applied Mathematics and Mechanics, 2026, 47(1): 113-122. doi: 10.21656/1000-0887.460090

Citation:

XIE Jianqiang, WANG Can. An Efficient Energy-Preserving Numerical Algorithm for Nonlinear Wave Equations[J]. Applied Mathematics and Mechanics, 2026, 47(1): 113-122. doi: 10.21656/1000-0887.460090

Citation:

XIE Jianqiang, WANG Can. An Efficient Energy-Preserving Numerical Algorithm for Nonlinear Wave Equations[J]. Applied Mathematics and Mechanics, 2026, 47(1): 113-122. doi: 10.21656/1000-0887.460090

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An Efficient Energy-Preserving Numerical Algorithm for Nonlinear Wave Equations

doi: 10.21656/1000-0887.460090

XIE Jianqiang^,,
WANG Can

School of Mathematical Sciences, Anhui University, Hefei 230601, P.R.China

Funds:

The National Science Foundation of China(12201005)

Received Date: 2025-05-06
Rev Recd Date: 2025-06-17

Available Online: 2026-01-21

Publish Date: 2026-01-01

Abstract

Abstract

An energy-preserving numerical algorithm, which is 2nd-order in time and 4th-order in space, for nonlinear wave equations was developed based on the order reduction method, the Lagrange multiplier method and the compact difference method. The discrete original energy conservation property of the suggested algorithm was proven. The computational procedure of the associated algorithm was exhibited. Numerical results validate the exactness and effectiveness of the proposed algorithm.
- nonlinear wave equation,
- order reduction method,
- Lagrange multiplier method,
- compact finite difference method,
- energy-preserving numerical algorithm

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References(23)

References

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