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Article Citation - WoS: 11Citation - Scopus: 20The Taylor Series Method and Trapezoidal Rule on Time Scales(Elsevier Science inc, 2020) Georgiev, Svetlin G.; Erhan, Inci M.The Taylor series method for initial value problems associated with dynamic equations of first order on time scales with delta differentiable graininess function is introduced. The trapezoidal rule for the same types of problems is derived and applied to specific examples. Numerical results are presented and discussed. (c) 2020 Elsevier Inc. All rights reserved.Article Citation - WoS: 2Citation - Scopus: 2The Taylor Series Method of Order p and Adams-Bashforth Method on Time Scales(Wiley, 2023) Georgiev, Svetlin G.; Erhan, Inci M.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.
