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

Fehaid Salem Alshammari ()
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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

Mathematics, 2024, vol. 12, issue 8, 1-17

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.

Keywords: variable coefficient reaction–diffusion free boundary value problem; future of oil prices; Chebyshev pseudospectral method; superconsistent Chebyshev collocation scheme; graded interval; error estimates (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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