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

doi:10.1016/j.aml.2015.01.008

Applied Mathematics Letters

Volume 45, July 2015, Pages 31-36

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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

Initial value problems

Variable mesh

Two-step explicit method

Damped wave equation

Region of absolute stability

Interval of periodicity

Interval of weak stability

Superstability

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^☆: Supported by ‘The Royal Society of Edinburgh’ under INSA-RSE Bilateral Exchange Program 2014.

Applied Mathematics Letters

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

Keywords