Innovative Approaches in Differential Equation Analysis Using the Enhanced Differential Transform and Homotopy Perturbation Method
Murugesh V. Priyadharshini M. Sharma Y.K. Lilhore U.K. Simaiya S. Tekeste L.G.
2026John Wiley and Sons Ltd
International Journal of Differential Equations
2026#2026Issue 1
Ordinary differential equations (ODEs) are very basic when it comes to modeling dynamic systems in various fields of science and engineering. However, solving high-dimensional, nonlinear, and stiff ODEs is still a major challenge given the limitations of existing numerical methods, which tend to have difficulties in terms of accuracy and efficiency. This paper presents a new numerical approach called the enhanced differential transform homotopy perturbation method (E-DTHPM), dedicated to overcoming the above difficulties. E-DTHPM presents a combination of the benefits of the differential transform method (DTM) and homotopy perturbation method (HPM) with an adaptive step sizing mechanism that is dynamic in step sizing based on local truncation errors (LTEs). The combination of these methods addresses an important research gap by offering an efficient and accurate solution to the IVP of ODEs with nonsmooth behaviors (singularities and discontinuity behaviors). The proposed method is an improvement over conventional techniques and will provide increased computational efficiency and precision for complicated high-dimensional systems. Numerical experiments show that E-DTHPM is better than existing methods and is useful for applications that need to be dynamic enough and accurate enough for fields such as physics, biology, and engineering. Copyright
adaptive step-sizing , differential transform , differential transform method (DTM) , homotopy perturbation , initial value problem , local truncation errors (LTEs) , numerical method
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School of Computer Science, Coventry University Kazakhstan, 3A, Korgalzhyn Highway, Astana, Kazakhstan
Department of Computer Science and Engineering, Faculty of Science and Technology (ICFAI Tech), ICFAI Foundations for Higher Education, Hyderabad, 501203, India
Department of CSE, Koneru Lakshmaiah Education Foundation, VaddeswaramAndhra Pradesh, Guntur, India
School of Computing Science and Engineering, Galgotias University, Uttar Pradesh, Greater Noida, India
School of Computer Applications and Technology, Galgotias University, Uttar Pradesh, Greater Noida, India
Eritrea Institute of Technology, Mai-Nefhi College, Himbrti, Mai Nefhi, Eritrea
School of Computer Science
Department of Computer Science and Engineering
Department of CSE
School of Computing Science and Engineering
School of Computer Applications and Technology
Eritrea Institute of Technology
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026