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Volume 19, Issue 2-3
A Stress Test for the Midpoint Time-Stepping Method

John Burkardt, Wenlong Pei & Catalin Trenchea

Int. J. Numer. Anal. Mod., 19 (2022), pp. 299-314.

Published online: 2022-04

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  • Abstract

The midpoint method can be implemented as a sequence of Backward Euler and Forward Euler solves with half time steps, allowing for improved performance of existing solvers for PDEs. We highlight the advantages of this refactorization by considering some specifics of implementation, conservation, error estimation, adaptivity, stability, and performance on several test problems.

  • Keywords

Midpoint method, local error estimation, time step adaptivity, conservation, B-stable.

  • AMS Subject Headings

34D20, 35L65, 65C20, 65D30, 65L07, 65L20, 65M12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-19-299, author = {Burkardt , JohnPei , Wenlong and Trenchea , Catalin}, title = {A Stress Test for the Midpoint Time-Stepping Method }, journal = {International Journal of Numerical Analysis and Modeling}, year = {2022}, volume = {19}, number = {2-3}, pages = {299--314}, abstract = {

The midpoint method can be implemented as a sequence of Backward Euler and Forward Euler solves with half time steps, allowing for improved performance of existing solvers for PDEs. We highlight the advantages of this refactorization by considering some specifics of implementation, conservation, error estimation, adaptivity, stability, and performance on several test problems.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/20482.html} }
TY - JOUR T1 - A Stress Test for the Midpoint Time-Stepping Method AU - Burkardt , John AU - Pei , Wenlong AU - Trenchea , Catalin JO - International Journal of Numerical Analysis and Modeling VL - 2-3 SP - 299 EP - 314 PY - 2022 DA - 2022/04 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/20482.html KW - Midpoint method, local error estimation, time step adaptivity, conservation, B-stable. AB -

The midpoint method can be implemented as a sequence of Backward Euler and Forward Euler solves with half time steps, allowing for improved performance of existing solvers for PDEs. We highlight the advantages of this refactorization by considering some specifics of implementation, conservation, error estimation, adaptivity, stability, and performance on several test problems.

Burkardt , JohnPei , Wenlong and Trenchea , Catalin. (2022). A Stress Test for the Midpoint Time-Stepping Method . International Journal of Numerical Analysis and Modeling. 19 (2-3). 299-314. doi:
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