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Multi-scale orthogonal basis method for nonlinear fractional equations with fractional integral boundary value conditions

Author

Listed:
  • Jiang, Wei
  • Chen, Zhong
  • Hu, Ning
  • Song, Haiyang
  • Yang, Zhaohong

Abstract

In this paper, we investigate the multi-scale orthogonal basis method for fractional integral boundary value problems. We apply the Newton iteration method to linearize the nonlinear problems and employees the idea of collocation method to determine the coefficients of multi-scale orthogonal basis, then the approximation solution is obtained. The error estimation and stable analysis are presented in detailed. The final numerical experiments verify that the accuracy of our method.

Suggested Citation

  • Jiang, Wei & Chen, Zhong & Hu, Ning & Song, Haiyang & Yang, Zhaohong, 2020. "Multi-scale orthogonal basis method for nonlinear fractional equations with fractional integral boundary value conditions," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    • Handle: RePEc:eee:apmaco:v:378:y:2020:i:c:s009630032030120x
    DOI: 10.1016/j.amc.2020.125151
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    References listed on IDEAS

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    1. Tofighi, Ali, 2003. "The intrinsic damping of the fractional oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(1), pages 29-34.
    2. Grudziński, Krzysztof & Żebrowski, Jan J, 2004. "Modeling cardiac pacemakers with relaxation oscillators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 153-162.
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