Linear multistep methods and global Richardson extrapolation

Imre Fekete; Lajos Lóczi

doi:10.1016/j.aml.2022.108267

Linear multistep methods and global Richardson extrapolation

Imre Fekete^*, Lajos Lóczi

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract (may include machine translation)

In this work, we study the application the classical Richardson extrapolation (RE) technique to accelerate the convergence of sequences resulting from linear multistep methods (LMMs) for solving initial-value problems of systems of ordinary diffe- rential equations numerically. The advantage of the LMM-RE approach is that the combined method possesses higher order and favorable linear stability properties in terms of A- or A(α)-stability, and existing LMM codes can be used without any modification.

Original language	English
Article number	108267
Journal	Applied Mathematics Letters
Volume	133
DOIs	https://doi.org/10.1016/j.aml.2022.108267
State	Published - Nov 2022
Externally published	Yes

Keywords

BDF methods
Convergence
Linear multistep methods
Region of absolute stability
Richardson extrapolation

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10.1016/j.aml.2022.108267License: CC BY-NC-ND

Fekete-Imre2_2022Publisher version, 711 KBLicense: CC BY-ND

Cite this

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title = "Linear multistep methods and global Richardson extrapolation",

abstract = "In this work, we study the application the classical Richardson extrapolation (RE) technique to accelerate the convergence of sequences resulting from linear multistep methods (LMMs) for solving initial-value problems of systems of ordinary diffe- rential equations numerically. The advantage of the LMM-RE approach is that the combined method possesses higher order and favorable linear stability properties in terms of A- or A(α)-stability, and existing LMM codes can be used without any modification.",

keywords = "BDF methods, Convergence, Linear multistep methods, Region of absolute stability, Richardson extrapolation",

author = "Imre Fekete and Lajos L{\'o}czi",

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language = "English",

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AU - Fekete, Imre

AU - Lóczi, Lajos

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AB - In this work, we study the application the classical Richardson extrapolation (RE) technique to accelerate the convergence of sequences resulting from linear multistep methods (LMMs) for solving initial-value problems of systems of ordinary diffe- rential equations numerically. The advantage of the LMM-RE approach is that the combined method possesses higher order and favorable linear stability properties in terms of A- or A(α)-stability, and existing LMM codes can be used without any modification.

KW - BDF methods

KW - Convergence

KW - Linear multistep methods

KW - Region of absolute stability

KW - Richardson extrapolation

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DO - 10.1016/j.aml.2022.108267

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JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

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ER -

Linear multistep methods and global Richardson extrapolation

Abstract (may include machine translation)

Keywords

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