Enriched reproducing kernel particle method for fractional advection–diffusion equation

Yuping Ying, Yanping Lian, Shaoqiang Tang*, Wing Kam Liu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


The reproducing kernel particle method (RKPM) has been efficiently applied to problems with large deformations, high gradients and high modal density. In this paper, it is extended to solve a nonlocal problem modeled by a fractional advection–diffusion equation (FADE), which exhibits a boundary layer with low regularity. We formulate this method on a moving least-square approach. Via the enrichment of fractional-order power functions to the traditional integer-order basis for RKPM, leading terms of the solution to the FADE can be exactly reproduced, which guarantees a good approximation to the boundary layer. Numerical tests are performed to verify the proposed approach.

Original languageEnglish (US)
Pages (from-to)515-527
Number of pages13
JournalActa Mechanica Sinica/Lixue Xuebao
Issue number3
StatePublished - Jun 1 2018


  • Advection–diffusion equation
  • Enriched reproducing kernel
  • Fractional calulus
  • Fractional-order basis
  • Meshfree method

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanical Engineering


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