Abstract
We propose a new high-order multi-stage method to solve the linear wave equation in an unconditionally energy stable manner. This Successive Multi-Stage (SMS) method is extended from the Crank–Nicolson method and unconditional energy conservation is guaranteed. We develop up to the sixth-order SMS method using the order conditions for Runge–Kutta methods and provide mathematical arguments showing that the SMS method is a different branch from well-known high order energy preserving methods for Hamiltonian systems. We present a proof of the unique solvability and numerically demonstrate the accuracy and stability of the proposed methods compared with comparisons.
Original language | English |
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Article number | 111098 |
Journal | Journal of Computational Physics |
Volume | 458 |
DOIs | |
State | Published - 1 Jun 2022 |
Bibliographical note
Publisher Copyright:© 2022 Elsevier Inc.
Keywords
- Energy conservation
- High-order time accuracy
- Linear wave equation
- Successive Multi-Stage (SMS) method