The Taylor Series Method of Order <i>p</I> and Adams-Bashforth Method on Time Scales

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Date

2023

Authors

Erhan, İnci

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Wiley

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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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$$ p $$ 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.

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ERHAN, INCI M./0000-0001-6042-3695
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ERHAN, INCI M. ORCID logo

Keywords

Adams-Bashforth method, delta derivative, dynamic equation, Taylor series method, time scale

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1

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Volume

46

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1

Start Page

304

End Page

320

URI

https://doi.org/10.1002/mma.8512
 https://hdl.handle.net/20.500.14411/2448

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