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Novel Numerical Investigation of Reaction Diffusion Equation Arising in Oil Price Modeling

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  • Fehaid Salem Alshammari

    (Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia)

Abstract

Consideration is given to a reaction–diffusion free boundary value problem with one or two turning points arising in oil price modeling. First, an exact (analytical) solution to the reduced problem (i.e., no diffusion term) was obtained for some given parameters. The space–time Chebyshev pseudospectral and superconsistent Chebyshev collocation method is proposed for both reaction diffusion (RDFBP) and reduced free boundary value problem. Error bounds on the discrete L 2 –norm and Sobolev norm ( H p ) are presented. Adaptively graded intervals were introduced and used according to the value of turning points to avoid the twin boundary layers phenomena. Excellent convergent (spectrally) and stable results for some special turning points were obtained for both reduced and RDFBP equations on an adaptively graded interval and this has been documented for the first time.

Suggested Citation

  • Fehaid Salem Alshammari, 2024. "Novel Numerical Investigation of Reaction Diffusion Equation Arising in Oil Price Modeling," Mathematics, MDPI, vol. 12(8), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1142-:d:1373373
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    References listed on IDEAS

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