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The Taylor series method of order $p$ and Adams-Bashforth method on time scales
  • Svetlin Georgiev,
  • Inci Erhan
Svetlin Georgiev
Sorbonne Universite

Corresponding Author:svetlingeorgiev1@gmail.com

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Inci Erhan
Atilim Universitesi
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Abstract

A recent study on the Taylor series method of second order and the trapezoidal rule for dynamic equations on time scales has been continued by introducing a derivation of the Taylor series method of arbitrary order $p$ on time scales. The error and convergence analysis of the method is also obtained. The 2 step Adams-Bashforth method for dynamic equations on time scales is concluded and applied to examples of initial value problems for nonlinear dynamic equations. Numerical results are presented and discussed.

Peer review status:Published

26 Nov 2021Submitted to Mathematical Methods in the Applied Sciences
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29 Nov 2021Submission Checks Completed
29 Nov 2021Assigned to Editor
03 Dec 2021Reviewer(s) Assigned
15 Mar 2022Review(s) Completed, Editorial Evaluation Pending
17 Mar 2022Editorial Decision: Revise Major
22 Mar 20221st Revision Received
23 Mar 2022Submission Checks Completed
23 Mar 2022Assigned to Editor
23 Mar 2022Review(s) Completed, Editorial Evaluation Pending
23 Mar 2022Editorial Decision: Revise Major
26 Mar 20222nd Revision Received
28 Mar 2022Submission Checks Completed
28 Mar 2022Assigned to Editor
28 Mar 2022Reviewer(s) Assigned
11 Jun 2022Review(s) Completed, Editorial Evaluation Pending
11 Jun 2022Editorial Decision: Accept
09 Jul 2022Published in Mathematical Methods in the Applied Sciences. 10.1002/mma.8512