### 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 |
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Pages (from-to) | 31-36 |

Number of pages | 6 |

Journal | Applied Mathematics Letters |

Volume | 45 |

Early online date | 22 Jan 2015 |

DOIs | |

Publication status | Published - 31 Jul 2015 |

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### 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

### Cite this

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**On the stability of two new two-step explicit methods for the numerical integration of second order initial value problem on a variable mesh.** / Mohanty, R.K.; McKee, Sean.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the stability of two new two-step explicit methods for the numerical integration of second order initial value problem on a variable mesh

AU - Mohanty, R.K.

AU - McKee, Sean

PY - 2015/7/31

Y1 - 2015/7/31

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 - http://www.scopus.com/inward/record.url?scp=84922377366&partnerID=8YFLogxK

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

U2 - 10.1016/j.aml.2015.01.008

DO - 10.1016/j.aml.2015.01.008

M3 - Article

AN - SCOPUS:84922377366

VL - 45

SP - 31

EP - 36

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

SN - 0893-9659

ER -