Alternative Legendre Polynomials Method for Nonlinear Fractional Integro-Differential Equations with Weakly Singular Kernel
| Autor: | Mingxu Yi, Yanlei Gong, Guodong Shi |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Article Subject
Differential equation General Mathematics MathematicsofComputing_NUMERICALANALYSIS Context (language use) 010103 numerical & computational mathematics 01 natural sciences 010101 applied mathematics Algebraic equation Nonlinear system Scheme (mathematics) Product (mathematics) Convergence (routing) ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION QA1-939 Applied mathematics 0101 mathematics Legendre polynomials Mathematics |
| Zdroj: | Journal of Mathematics, Vol 2021 (2021) |
| ISSN: | 2314-4629 |
| DOI: | 10.1155/2021/9968237 |
| Popis: | In this paper, we present a numerical scheme for finding numerical solution of a class of weakly singular nonlinear fractional integro-differential equations. This method exploits the alternative Legendre polynomials. An operational matrix, based on the alternative Legendre polynomials, is derived to be approximated the singular kernels of this class of the equations. The operational matrices of integration and product together with the derived operational matrix are utilized to transform nonlinear fractional integro-differential equations to the nonlinear system of algebraic equations. Furthermore, the proposed method has also been analyzed for convergence, particularly in context of error analysis. Moreover, results of essential numerical applications have also been documented in a graphical as well as tabular form to elaborate the effectiveness and accuracy of the proposed method. |
| Databáze: | OpenAIRE |
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