Applications of modified Bessel polynomials to solve a nonlinear choatic fractional-order system in the financial market: Domain-splitting collocation techniques

dc.contributor.authorIzadi, Mohammad
dc.contributor.authorSrivastava, Hari Mohan
dc.date.accessioned2024-01-23T23:16:31Z
dc.date.available2024-01-23T23:16:31Z
dc.date.copyright2023en_US
dc.date.issued2023
dc.description.abstractWe propose two accurate and efficient spectral collocation techniques based on a (novel) domain-splitting strategy to handle a nonlinear fractional system consisting of three ODEs arising in financial modeling and with chaotic behavior. One of the major numerical difficulties in designing traditional spectral methods is in the handling of model problems on a long computational domain, which usually yields to loss of accuracy. One remedy is to split the underlying domain and apply the spectral method locally in each subdomain rather than on the global domain of interest. To treat the chaotic financial system numerically, we use the generalized version of modified Bessel polynomials (GMBPs) in the collocation matrix approaches along with the domain-splitting strategy. Whereas the first matrix collocation scheme is directly applied to the financial model problem, the second one is a combination of the quasilinearization method and the direct first numerical matrix method. In the former approach, we arrive at nonlinear algebraic matrix equations while the resulting systems are linear in the latter method and can be solved more efficiently. A convergence theorem related to GMBPs is proved and an upper bound for the error is derived. Several simulation outcomes are provided to show the utility and applicability of the presented matrix collocation procedures.en_US
dc.description.reviewstatusRevieweden_US
dc.description.scholarlevelFacultyen_US
dc.identifier.citationIzadi, M., & Srivastava, H. M. (2023). Applications of modified Bessel polynomials to solve a nonlinear chaotic fractional-order system in the financial market: Domain-splitting collocation techniques. Computation, 11(7), 130. https://doi.org/10.3390/computation11070130en_US
dc.identifier.urihttps://doi.org/10.3390/computation11070130
dc.identifier.urihttp://hdl.handle.net/1828/15849
dc.language.isoenen_US
dc.publisherComputationen_US
dc.subjectcollocation pointsen_US
dc.subjectLiouville-Caputo fractional operatoren_US
dc.subjectchaotic systemen_US
dc.subjectconvergent analysisen_US
dc.subjectfinancial modelen_US
dc.subjectmodified Bessel functionsen_US
dc.titleApplications of modified Bessel polynomials to solve a nonlinear choatic fractional-order system in the financial market: Domain-splitting collocation techniquesen_US
dc.typeArticleen_US

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