A new implicit-explicit local differential method for boundary value problems

Hüseyin Tunç, Murat Sari*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In this study, an effective numerical method based on Taylor expansions is presented for boundary value problems. This method is arbitrary directional and called as implicit-explicit local differential transform method (IELDTM). With the completion of this study, a reliable numerical method is derived by optimizing the required degrees of freedom. It is shown that the order refinement procedure of the IELDTM does not affect the degrees of freedom. A priori error analysis of the current method is constructed and order conditions are presented in a detailed analysis. The theoretical order expectations are verified for nonlinear BVPs. Stability of the IELDTM is investigated by following the analysis of approximation matrices. To illustrate efficiency of the method, qualitative and quantitative results are presented for various challenging BVPs. It is tested that the current method is reliable and accurate for a broad range of problems even for strongly nonlinear and singularly perturbed BVPs. The produced results have revealed that the IELDTM is more accurate than the existing ones in literature.

Original languageEnglish
Pages (from-to)742-766
Number of pages25
JournalTurkish Journal of Mathematics
Volume45
Issue number2
DOIs
Publication statusPublished - 2021
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2021. TÜBİTAK.

Keywords

  • boundary value problem
  • Implicit-explicit methods
  • numerical algorithms
  • stiff problems
  • Taylor series

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