A variable step-size exponentially fitted explicit hybrid method for solving oscillatory problems

Samat Faieza, F. Ismail, M. B. Suleiman

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1 Citation (Scopus)

Abstract

An exponentially fitted explicit hybrid method for solving oscillatory problems is obtained. This method has four stages. The first three stages of the method integrate exactly differential systems whose solutions can be expressed as linear combinations of {1,x,exp(μx),exp(-μx)},μ ∈ C, while the last stage of this method integrates exactly systems whose solutions are linear combinations of {1,x,x 2,x 3,x 4,exp(μx),exp(- μx)}. This method is implemented in variable step-size code basing on an embedding approach. The stability analysis is given. Numerical experiments that have been carried out show the efficiency of our method.

Original languageEnglish
Article number328197
JournalInternational Journal of Mathematics and Mathematical Sciences
Volume2011
DOIs
Publication statusPublished - 2011
Externally publishedYes

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Variable Step Size
Explicit Methods
Hybrid Method
Linear Combination
Integrate
Differential System
Stability Analysis
Numerical Experiment

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

Cite this

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abstract = "An exponentially fitted explicit hybrid method for solving oscillatory problems is obtained. This method has four stages. The first three stages of the method integrate exactly differential systems whose solutions can be expressed as linear combinations of {1,x,exp(μx),exp(-μx)},μ ∈ C, while the last stage of this method integrates exactly systems whose solutions are linear combinations of {1,x,x 2,x 3,x 4,exp(μx),exp(- μx)}. This method is implemented in variable step-size code basing on an embedding approach. The stability analysis is given. Numerical experiments that have been carried out show the efficiency of our method.",
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AB - An exponentially fitted explicit hybrid method for solving oscillatory problems is obtained. This method has four stages. The first three stages of the method integrate exactly differential systems whose solutions can be expressed as linear combinations of {1,x,exp(μx),exp(-μx)},μ ∈ C, while the last stage of this method integrates exactly systems whose solutions are linear combinations of {1,x,x 2,x 3,x 4,exp(μx),exp(- μx)}. This method is implemented in variable step-size code basing on an embedding approach. The stability analysis is given. Numerical experiments that have been carried out show the efficiency of our method.

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