https://semarakilmu.com.my/journals/index.php/sijfam <p>The Semarak International Journal of Fundamental and Applied Mathematics (SIJFAM) is an open-access, double-blind refereed academic journal with the aim to provide an international platform for those in academic and scientific community by publishing original articles as well as reviews in topics related to the field of pure and applied mathematics. Scope of the journal is related to mathematical sciences, covering topics in the areas but not limited to theoretical and applied mathematics, statistics, industrial mathematics, biomathematics, mathematics education, ethnomathematics, history of mathematics and their related fields.</p> <p> </p> en-US Semarak International Journal of Fundamental and Applied Mathematics https://semarakilmu.com.my/journals/index.php/sijfam/article/view/8964 <p>This paper introduces a novel method called the Adaptive Hybrid Reduced Differential Transform Method (AHRDTM) to solve Nonlinear Schrödinger Equations (NLSEs). This method provides semi-analytical solutions over a longer time frame. It achieves this by producing sub-division intervals of varying lengths, distinguishing it from the classical Multistep Reduced Differential Transform Method (MsRDTM). Importantly, the AHRDTM eliminates the necessity for perturbation, linearization, or discretization, providing the benefits of adaptability and reliability. The outcomes exhibit that AHRDTM yields highly efficient solutions for NLSEs. Moreover, the method is simple, significantly reducing the computational workload in solving NLSE problems, and shows promising opportunity for application in diverse complex partial differential equations (PDEs). The efficiency and effectiveness of AHRDTM are demonstrated through tables and graphical representations.</p> Abdul Rahman Farhan Sabdin Che Haziqah Che Hussin Arif Mandangan Jumat Sulaiman Copyright (c) 2024 Semarak International Journal of Fundamental and Applied Mathematics 2024-05-29 2024-05-29 2 1 1 12