Energy conserving successive multi-stage method for the linear wave equation

Jaemin Shin, June Yub Lee

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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 languageEnglish
Article number111098
JournalJournal of Computational Physics
StatePublished - 1 Jun 2022

Bibliographical note

Publisher Copyright:
© 2022 Elsevier Inc.


  • Energy conservation
  • High-order time accuracy
  • Linear wave equation
  • Successive Multi-Stage (SMS) method


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