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

Hüseyin TUNÇ, (Yıldız Teknik Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, İstanbul, Türkiye)
Murat SARI (Yıldız Teknik Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, İstanbul, Türkiye)
Turkish Journal of Mathematics
2 0
Yıl: 2021 Cilt: 45 Sayı: 2 Sayfa Aralığı: 742 - 766 Metin Dili: İngilizce DOI: 10.3906/mat-2009-68 İndeks Tarihi: 22-09-2021

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

Öz:
In this study, an effective numerical method based on Taylor expansions is presented for boundary valueproblems. 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 degreesof freedom. It is shown that the order refinement procedure of the IELDTM does not affect the degrees of freedom. Apriori error analysis of the current method is constructed and order conditions are presented in a detailed analysis. Thetheoretical order expectations are verified for nonlinear BVPs. Stability of the IELDTM is investigated by followingthe analysis of approximation matrices. To illustrate efficiency of the method, qualitative and quantitative results arepresented for various challenging BVPs. It is tested that the current method is reliable and accurate for a broad rangeof problems even for strongly nonlinear and singularly perturbed BVPs. The produced results have revealed that theIELDTM is more accurate than the existing ones in literature.
Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
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APA Tunc H, Sari M (2021). A new implicit-explicit local differential method for boundary value problems. , 742 - 766. 10.3906/mat-2009-68
Chicago Tunc Huseyin,Sari Murat A new implicit-explicit local differential method for boundary value problems. (2021): 742 - 766. 10.3906/mat-2009-68
MLA Tunc Huseyin,Sari Murat A new implicit-explicit local differential method for boundary value problems. , 2021, ss.742 - 766. 10.3906/mat-2009-68
AMA Tunc H,Sari M A new implicit-explicit local differential method for boundary value problems. . 2021; 742 - 766. 10.3906/mat-2009-68
Vancouver Tunc H,Sari M A new implicit-explicit local differential method for boundary value problems. . 2021; 742 - 766. 10.3906/mat-2009-68
IEEE Tunc H,Sari M "A new implicit-explicit local differential method for boundary value problems." , ss.742 - 766, 2021. 10.3906/mat-2009-68
ISNAD Tunc, Huseyin - Sari, Murat. "A new implicit-explicit local differential method for boundary value problems". (2021), 742-766. https://doi.org/10.3906/mat-2009-68
APA Tunc H, Sari M (2021). A new implicit-explicit local differential method for boundary value problems. Turkish Journal of Mathematics, 45(2), 742 - 766. 10.3906/mat-2009-68
Chicago Tunc Huseyin,Sari Murat A new implicit-explicit local differential method for boundary value problems. Turkish Journal of Mathematics 45, no.2 (2021): 742 - 766. 10.3906/mat-2009-68
MLA Tunc Huseyin,Sari Murat A new implicit-explicit local differential method for boundary value problems. Turkish Journal of Mathematics, vol.45, no.2, 2021, ss.742 - 766. 10.3906/mat-2009-68
AMA Tunc H,Sari M A new implicit-explicit local differential method for boundary value problems. Turkish Journal of Mathematics. 2021; 45(2): 742 - 766. 10.3906/mat-2009-68
Vancouver Tunc H,Sari M A new implicit-explicit local differential method for boundary value problems. Turkish Journal of Mathematics. 2021; 45(2): 742 - 766. 10.3906/mat-2009-68
IEEE Tunc H,Sari M "A new implicit-explicit local differential method for boundary value problems." Turkish Journal of Mathematics, 45, ss.742 - 766, 2021. 10.3906/mat-2009-68
ISNAD Tunc, Huseyin - Sari, Murat. "A new implicit-explicit local differential method for boundary value problems". Turkish Journal of Mathematics 45/2 (2021), 742-766. https://doi.org/10.3906/mat-2009-68
Sayfa Oluşturulma Tarihi
23-04-2024 19:18

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