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Improved spectral deferred correction methods for fractional differential equations

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  • Yang, Changqing

Abstract

In this study, we improved the spectral deferred correction method for nonlinear fractional differential equations. First, problems were transformed into equivalent nonlinear Volterra integral equations with weakly singular kernels. We then employed the fractional Adams–Bashforth method in the prediction step and used the Gauss quadrature formula and fractional Adams–Moulton scheme in the correction step. Moreover, a vigorous error analysis for the numerical scheme was conducted. Finally, computational results for some experiments were reported to demonstrate the accuracy and ease of implementation of the improved numerical scheme.

Suggested Citation

  • Yang, Changqing, 2023. "Improved spectral deferred correction methods for fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    • Handle: RePEc:eee:chsofr:v:168:y:2023:i:c:s0960077923001054
    DOI: 10.1016/j.chaos.2023.113204
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    1. Vladislav N. Kovalnogov & Ruslan V. Fedorov & Tamara V. Karpukhina & Theodore E. Simos & Charalampos Tsitouras, 2022. "Runge–Kutta Embedded Methods of Orders 8(7) for Use in Quadruple Precision Computations," Mathematics, MDPI, vol. 10(18), pages 1-12, September.
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    6. Pourbabaee, Marzieh & Saadatmandi, Abbas, 2022. "A new operational matrix based on Müntz–Legendre polynomials for solving distributed order fractional differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 210-235.
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