Adaptive hybrid reduced differential transform method in solving nonlinear schrodinger equations

Abdul Rahman Farhan Sabdin and Che Haziqah Che Hussin and Jumat Sulaiman and Arif Mandangan and Essam Roshdy El-Zahar (2025) Adaptive hybrid reduced differential transform method in solving nonlinear schrodinger equations. Journal of Advanced Research Design, 129 (1). pp. 1-13. ISSN 2462-1943

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Abstract

In this paper, piecewise-analytical and numerical solutions are obtained by a new adapted approach named the Adaptive Hybrid Reduced Differential Transform Method (AHRDTM). The fundamentals of the method are introduced, followed by its application to Nonlinear Schrodinger Equations (NLSEs). Analytical and numerical solutions are acquired using piecewise convergent series with computationally feasible components across a sequence of sub-intervals of varying length. This succeeds due to the adaptive algorithm introduced and the substitution of the non-linear term in the NLSEs with their corresponding Adomian polynomials. The accuracy of the AHRDTM is observed through numerical comparisons between the proposed method and the Modified Reduced Differential Transform Method (MRDTM) with their respective exact solutions. The absolute errors presented in the table reveal that the proposed approach has better accuracy in solving the considered equations. The results and pictorial illustrations have been provided to demonstrate the reliability of the method’s accuracy in obtaining approximate solutions.

Item Type:	Article
Keyword:	Adaptive multistep differential transform method; multistep reduced differential transform method; nonlinear Schrodinger equations; adaptive algorithm; Adomian polynomials
Subjects:	Q Science > QA Mathematics > QA1-939 Mathematics > QA299.6-433 Analysis Q Science > QA Mathematics > QA1-939 Mathematics > QA71-90 Instruments and machines > QA75-76.95 Calculating machines
Department:	FACULTY > Faculty of Science and Natural Resources
Depositing User:	ABDULLAH BIN SABUDIN -
Date Deposited:	18 Jun 2025 10:40
Last Modified:	18 Jun 2025 10:40
URI:	https://eprints.ums.edu.my/id/eprint/44197

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