Numerical Solutions of the Multi-Space Fractional-Order Coupled Korteweg–De Vries Equation with Several Different Kernels

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dc.contributor.authorSaad, Khaled M.
dc.contributor.authorSrivastava, Hari M.
dc.date.accessioned2023-10-15T16:58:10Z
dc.date.available2023-10-15T16:58:10Z
dc.date.copyright2023en_US
dc.date.issued2023
dc.description.abstractIn this article, the authors propose to investigate the numerical solutions of several fractional-order models of the multi-space coupled Korteweg–De Vries equation involving many different kernels. In order to transform these models into a set or system of differential equations, various properties of the first-kind Chebyshev polynomial are used in this study. The main objective of the present study is to apply the spectral collocation approach for the multi-space fractional-order coupled Korteweg–De Vries equation with different kernels. We use finite differences to numerically solve these differential equations by reducing them to algebraic equations. The Newton (or, more precisely, the Newton–Raphson) method is then used to solve these resulting algebraic equations. By calculating the error involved in our approach, the precision of the numerical solution is verified. The use of spectral methods, which provide excellent accuracy and exponential convergence for issues with smooth solutions, is shown to be a benefit of the current study.en_US
dc.description.reviewstatusRevieweden_US
dc.description.scholarlevelFacultyen_US
dc.description.sponsorshipThis research was funded by the Deanship of Scientific Research at Najran University under grant number (NU/DRP/SERC/12/16).en_US
dc.identifier.citationSaad, K. M., & Srivastava, H. M. (2023). Numerical Solutions of the Multi-Space Fractional-Order Coupled Korteweg–De Vries Equation with Several Different Kernels. Fractal and Fractional, 7(10), 716. https://doi.org/10.3390/fractalfract7100716en_US
dc.identifier.urihttps://doi.org/10.3390/fractalfract7100716
dc.identifier.urihttp://hdl.handle.net/1828/15532
dc.language.isoenen_US
dc.publisherFractal and Fractionalen_US
dc.subjectmulti-space fractional-order coupled Korteweg�De Vries equation
dc.subjectChebyshev polynomials of the first kind
dc.subjectChebyshev spectral collocation method
dc.subjectNewton�Raphson method
dc.subjectoperators of fractional calculus
dc.subjectRiemann�Liouville and Liouville�Caputo fractional derivatives
dc.subjectCaputo�Fabrizio and Atangana�Baleanu fractional derivatives
dc.subject.departmentDepartment of Mathematics and Statistics
dc.titleNumerical Solutions of the Multi-Space Fractional-Order Coupled Korteweg–De Vries Equation with Several Different Kernelsen_US
dc.typeArticleen_US

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