A Padé–Legendre Reconstruction Approach in Capturing Shock Behaviour

Huseyin Tunc, Murat Sari*, Sufii H. Mussa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Many numerical methods for solving partial differential equations having shock behaviour produce unphysical oscillations. This study aims to prove the efficiency of applying Padé-Legendre reconstruction technique for stabilization of these oscillations. To get better, physically acceptable solutions of the advection dominated Burgers equation, the fourth-order finite difference method (FD4) and the Padé-Legendre reconstruction technique (PLR) are combined. The PLR is designed for the stabilization process of discrete solutions produced by the FD4 with the use of suitable composite numerical integrations. It has been proved that the present approach can capture shock behaviours as well as minimize the maximum errors produced by FD4. Two challenging test problems having shock behaviours are considered, and the positive effect of the PLR is illustrated.

Original languageEnglish
Pages (from-to)45-60
Number of pages16
JournalAzerbaijan Journal of Mathematics
Issue number2
Publication statusPublished - Jul 2022
Externally publishedYes

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  • compact finite difference
  • nonlinear advection diffusion process
  • nonlinear modelling
  • Padé-Legendre reconstruction
  • shock behaviour


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