Geodesic
Stability properties of fractional second linear multistep methods in the implicit form: theory and applications
Filomat, Tome 37 (2023) no. 21, p. 7241

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

DOI

The main purpose of this paper is to numerically solve the fractional differential equations (FDE)s with the fractional order in (1, 2) using the implicit forms of the special case of fractional second linear multistep methods (FSLMM)s. The studies are focused on the stability properties and proving that the proposed methods are A(α)−stable. For this purpose, after introducing the FSLMMs, the implicit family of FSLMMs based on fractional backward difference formula 1 (FBDF1) are constructed which have the first, and second order of convergence.The stability regions of the proposed methods are thoroughly studied. Furthermore, in order to show the validity of the proposed theories, some numerical examples are reported. Finally, the application of proposed method for solving the Bagley-Torvik (B-T) equation is also presented.
DOI : 10.2298/FIL2321241I
Classification : 65L99, 26A33
Keywords: Fractional second linear multistep method, stability properties, Caputo fractional derivative, A(α)−stable, Bagley-Torvik equation 
Safar Irandoust-Pakchin; Somaiyeh Abdi-Mazraeh; Shahram Rezapour. Stability properties of fractional second linear multistep methods in the implicit form: theory and applications. Filomat, Tome 37 (2023) no. 21, p. 7241 . doi: 10.2298/FIL2321241I
@article{10_2298_FIL2321241I,
     author = {Safar Irandoust-Pakchin and Somaiyeh Abdi-Mazraeh and Shahram Rezapour},
     title = {Stability properties of fractional second linear multistep methods in the implicit form: theory and applications},
     journal = {Filomat},
     pages = {7241 },
     year = {2023},
     volume = {37},
     number = {21},
     doi = {10.2298/FIL2321241I},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2321241I/}
}
TY  - JOUR
AU  - Safar Irandoust-Pakchin
AU  - Somaiyeh Abdi-Mazraeh
AU  - Shahram Rezapour
TI  - Stability properties of fractional second linear multistep methods in the implicit form: theory and applications
JO  - Filomat
PY  - 2023
SP  - 7241 
VL  - 37
IS  - 21
UR  - http://geodesic.mathdoc.fr/articles/10.2298/FIL2321241I/
DO  - 10.2298/FIL2321241I
LA  - en
ID  - 10_2298_FIL2321241I
ER  - 
%0 Journal Article
%A Safar Irandoust-Pakchin
%A Somaiyeh Abdi-Mazraeh
%A Shahram Rezapour
%T Stability properties of fractional second linear multistep methods in the implicit form: theory and applications
%J Filomat
%D 2023
%P 7241 
%V 37
%N 21
%U http://geodesic.mathdoc.fr/articles/10.2298/FIL2321241I/
%R 10.2298/FIL2321241I
%G en
%F 10_2298_FIL2321241I

Cité par Sources :