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 language | English |
|---|---|
| Pages (from-to) | 742-766 |
| Number of pages | 25 |
| Journal | Turkish Journal of Mathematics |
| Volume | 45 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2021 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2021. TÜBİTAK.
Funding
The authors thank the anonymous referees of the Turkish Journal of Mathematics for their valuable comments and suggestions to improve the article. The first author would like to thank the Science Fellowships and Grant Programmes Department of TÜBİTAK (BİDEB) for their financial support to his academic research. The second author thanks Dr. Aniela Balacescu (Constantin Brâncuşi University of Târgu Jiu, Romania) for the great hospitality during the conference. The authors thank the anonymous referees of the Turkish Journal of Mathematics for their valuable comments and suggestions to improve the article. The first author would like to thank the Science Fellowships and Grant Programmes Department of T?B?TAK (B?DEB) for their financial support to his academic research. The second author thanks Dr. Aniela Balacescu (Constantin Br?ncu?i University of T?rgu Jiu, Romania) for the great hospitality during the conference.
| Funders | Funder number |
|---|---|
| Programmes Department of T?B?TAK | |
| Programmes Department of TÜBİTAK |
Keywords
- Implicit-explicit methods
- Taylor series
- boundary value problem
- numerical algorithms
- stiff problems