Numerical approach of the nonlinear reaction-advection-diffusion equation with time-space conformable fractional derivatives
| Autor: | Nouiri Brahim |
|---|---|
| Přispěvatelé: | Maltepe Üniversitesi, İnsan ve Toplum Bilimleri Fakültesi |
| Rok vydání: | 2021 |
| Předmět: |
Chebyshev polynomials
Series (mathematics) Shifted Chebyshev polynomials of the fourth kind Finite difference method Conformable matrix Fractional calculus symbols.namesake Nonlinear system Dirichlet boundary condition Reaction-advection-diffusion equation symbols Applied mathematics Convection–diffusion equation Conformable fractional calculus Mathematics |
| Zdroj: | FOURTH INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2020). |
| ISSN: | 0094-243X |
| DOI: | 10.1063/5.0042459 |
| Popis: | In this paper, a numerical approach is proposed for solving one dimensional nonlinear time-space-fractional reaction-advection-diffusion equation with Dirichlet boundary conditions. The fractional derivatives are described in the conformable sense. The numerical scheme is based on shifted Chebyshev polynomials of the fourth kind. The unknown function is written as Cheby-shev series with m terms. The nonlinear space fractional reaction-advection-diffusion equation is reduced to a system of nonlinear ordinary differential equations by using the properties of Chebyshev polynomials and conformable fractional calculus.The finite difference method is applied to solve this system. Finally, numerical example is presented to confirm the reliability and effectiveness of the proposed approach. |
| Databáze: | OpenAIRE |
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