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Rufai, Uthman, Sibanda, Precious, Goqo, Sicelo. (1405). An overlapping adaptive step-size multi-derivative hybrid block method for higher order initial value problems. سامانه مدیریت نشریات علمی, 14(2), 798-827. doi: 10.22034/cmde.2025.63158.2817
Uthman Olamide Rufai; Precious Sibanda; Sicelo Goqo. "An overlapping adaptive step-size multi-derivative hybrid block method for higher order initial value problems". سامانه مدیریت نشریات علمی, 14, 2, 1405, 798-827. doi: 10.22034/cmde.2025.63158.2817
Rufai, Uthman, Sibanda, Precious, Goqo, Sicelo. (1405). 'An overlapping adaptive step-size multi-derivative hybrid block method for higher order initial value problems', سامانه مدیریت نشریات علمی, 14(2), pp. 798-827. doi: 10.22034/cmde.2025.63158.2817
Rufai, Uthman, Sibanda, Precious, Goqo, Sicelo. An overlapping adaptive step-size multi-derivative hybrid block method for higher order initial value problems. سامانه مدیریت نشریات علمی, 1405; 14(2): 798-827. doi: 10.22034/cmde.2025.63158.2817

An overlapping adaptive step-size multi-derivative hybrid block method for higher order initial value problems

Computational Methods for Differential Equations
مقاله 20، دوره 14، شماره 2، تیر 2026، صفحه 798-827    اصل مقاله (974.55 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.63158.2817
نویسندگان
Uthman Olamide Rufai* ؛ Precious Sibanda؛ Sicelo Goqo
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Pietermaritzburg 3201, South Africa.
چکیده
The need for accurate solutions to mathematical models, particularly for linear and nonlinear higher-order initial value problems, is essential across various scientific and engineering fields. Traditional methods often face challenges with stability and precision, especially in non-linear cases, prompting the development of advanced numerical techniques. This study introduces a two-step overlapping adaptive step-size multi-derivative hybrid block method to address these challenges in solving higher-order initial value problems. The method incorporates overlapping elements, using the second-to-last intra-step point from the previous step within each integration block to enhance accuracy. The method uses error estimation and selects an appropriate step-size, ensuring the desired accuracy without wasting computational resources or introducing unnecessary errors. The non-linear initial value problems are efficiently linearized using a modified-Picard iteration. Numerical examples are provided to demonstrate the efficiency and accuracy of the proposed method, and its performance is compared against a similar non-overlapping method as well as other methods reported in the literature.
کلیدواژه‌ها
Hybrid block method؛ Multi-derivative؛ Modified-Picard iteration؛ Overlapping؛ Adaptive step-size
مراجع
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