On the stability of two new two-step explicit methods for the numerical integration of second order initial value problem on a variable mesh

R.K. Mohanty; Sean McKee

doi:10.1016/j.aml.2015.01.008

On the stability of two new two-step explicit methods for the numerical integration of second order initial value problem on a variable mesh

R.K. Mohanty, Sean McKee

Mathematics And Statistics

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8 Citations (Scopus)

Abstract

We present two novel two-step explicit methods for the numerical solution of the second order initial value problem on a variable mesh. In the case of a constant mesh the method is superstable in the sense of Chawla (1985). Numerical experimentation is provided to verify the stability analysis.

Original language	English
Pages (from-to)	31-36
Number of pages	6
Journal	Applied Mathematics Letters
Volume	45
Early online date	22 Jan 2015
DOIs	https://doi.org/10.1016/j.aml.2015.01.008
Publication status	Published - 31 Jul 2015

Funding

This research was supported by ‘ The Royal Society of Edinburgh ’ under INSA-RSE Bilateral Exchange Program 2014. The authors thank the reviewers for their valuable suggestions, which have substantially improved the standard of the paper.

Keywords

damped wave equation
initial value problems
interval of periodicity
interval of weak stability
region of absolute stability
superstability
two-step explicit method
variable mesh

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10.1016/j.aml.2015.01.008

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abstract = "We present two novel two-step explicit methods for the numerical solution of the second order initial value problem on a variable mesh. In the case of a constant mesh the method is superstable in the sense of Chawla (1985). Numerical experimentation is provided to verify the stability analysis.",

keywords = "damped wave equation, initial value problems, interval of periodicity, interval of weak stability, region of absolute stability, superstability, two-step explicit method, variable mesh",

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AU - Mohanty, R.K.

AU - McKee, Sean

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N2 - We present two novel two-step explicit methods for the numerical solution of the second order initial value problem on a variable mesh. In the case of a constant mesh the method is superstable in the sense of Chawla (1985). Numerical experimentation is provided to verify the stability analysis.

AB - We present two novel two-step explicit methods for the numerical solution of the second order initial value problem on a variable mesh. In the case of a constant mesh the method is superstable in the sense of Chawla (1985). Numerical experimentation is provided to verify the stability analysis.

KW - damped wave equation

KW - initial value problems

KW - interval of periodicity

KW - interval of weak stability

KW - region of absolute stability

KW - superstability

KW - two-step explicit method

KW - variable mesh

UR - https://www.scopus.com/pages/publications/84922377366

UR - https://www.sciencedirect.com/journal/applied-mathematics-letters

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EP - 36

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

ER -

On the stability of two new two-step explicit methods for the numerical integration of second order initial value problem on a variable mesh

Abstract

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Keywords

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