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- W3125988921 abstract "This paper proposes a method based on two-dimensional Euler polynomials combined with Gauss-Jacobi quadrature formula. The method is used to solve two-dimensional Volterra integral equations with fractional order weakly singular kernels. Firstly, we prove the existence and uniqueness of the original equation by Gronwall inequality and mathematical induction method. Secondly, we use two-dimensional Euler polynomials to approximate the unknown function of the original equation, and the Gauss-Jacobi quadrature formula is used to approximate the integrals in the original equation. Thirdly, we prove the existence and uniqueness of the solution of approximate equation, and the error analysis of the proposed method is given. Finally, some numerical examples illustrate the efficiency of the method." @default.
- W3125988921 created "2021-02-01" @default.
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- W3125988921 date "2021-05-01" @default.
- W3125988921 modified "2023-09-23" @default.
- W3125988921 title "Two-dimensional Euler polynomials solutions of two-dimensional Volterra integral equations of fractional order" @default.
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- W3125988921 doi "https://doi.org/10.1016/j.apnum.2021.01.007" @default.
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