Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 52 min ago
PreprintCC BY 4.0arXiv

Optimized linear multistep methods for stiff problems

  • Tyler Jensen
  • David I Ketcheson
  • Lajos Lóczi
Open at sourcePDFDOICite

Abstract

We design and test several new optimized linear multistep methods for stiff problems. Each method is A-stable, implicit, and second-order accurate. We focus on achieving the smallest possible error constant while also ensuring that stiff modes are damped. We recover some known optimal L-stable three- and four-step methods, and provide new and improved five-step methods. We also develop new methods that are not L-stable but provide a prescribed rate of damping in the infinitely stiff limit. Variable-step-size formulae are also provided for some of the new methods. Numerical tests demonstrate that the improved error constants lead to improved accuracy.

Related

  1. Stability and Error Analysis of Multistep IMEX Local Discontinuous Galerkin Methods for One-Dimensional Nonlinear Fourth-Order Evolution Problems
    Amjad G. Alharbi, Tarek Aboelenen
    MathematicsPeer-reviewedCC BY 4.0General mathematicsCrossref
  2. On randomized batch-sampling coordinate descent methods for solving linear least-squares problems
    Dong-Yue Xie, Xi Yang
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingOptimisation & controlarXiv
  3. A semi-generating function approach to the stability of implicit-explicit multistep methods for nonlinear parabolic equations
    Hong-lin Liao, Chaoyu Quan, Tao Tang +1
    arXivPreprintCC BY-NC-ND 4.0Full textNumerical analysis & scientific computingarXiv
  4. Linear and non-linear thermal system identification based on the integral of non-integer order — Application to solve inverse heat conduction linear and non-linear problems
    Jean-Luc Battaglia
    International Journal of Thermal SciencesPeer-reviewedLicence not stated7 citedMathematical physicsHAL
  5. Average Energy Dissipation Rates of Implicit-Explicit Runge-Kutta Methods for Gradient Flow Problems
    Hong-lin Liao, Xuping Wang, Cao Wen
    CSIAM Transactions on Applied MathematicsPeer-reviewedLicence not stated6 citedNumerical analysis & scientific computingOpenAlex

Cite

BibTeXRIS
BibTeX
@misc{jensen2026optimized,
  title = {{Optimized linear multistep methods for stiff problems}},
  author = {Tyler Jensen and David I Ketcheson and Lajos Lóczi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.22685},
  eprint = {2610.22685},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.22685},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Optimized linear multistep methods for stiff problems
AU  - Tyler Jensen
AU  - David I Ketcheson
AU  - Lajos Lóczi
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.22685
UR  - https://arxiv.org/abs/2610.22685
AB  - We design and test several new optimized linear multistep methods for stiff problems. Each method is A-stable, implicit, and second-order accurate. We focus on achieving the smallest possible error constant while also ensuring that stiff modes are damped. We recover some known optimal L-stable three- and four-step methods, and provide new and improved five-step methods. We also develop new methods that are not L-stable but provide a prescribed rate of damping in the infinitely stiff limit. Variable-step-size formulae are also provided for some of the new methods. Numerical tests demonstrate that the improved error constants lead to improved accuracy.
ER  -