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Rufai, Uthman, Sibanda, Precious, Goqo, Sicelo. (1404). AN OVERLAPPING ADAPTIVE STEP-SIZE MULTI-DERIVATIVE HYBRID BLOCK METHOD FOR HIGHER ORDER INITIAL VALUE PROBLEMS. سامانه مدیریت نشریات علمی, (), -. 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, , , 1404, -. doi: 10.22034/cmde.2025.63158.2817
Rufai, Uthman, Sibanda, Precious, Goqo, Sicelo. (1404). 'AN OVERLAPPING ADAPTIVE STEP-SIZE MULTI-DERIVATIVE HYBRID BLOCK METHOD FOR HIGHER ORDER INITIAL VALUE PROBLEMS', سامانه مدیریت نشریات علمی, (), pp. -. 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, 1404; (): -. 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
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 31 فروردین 1404    اصل مقاله (1.69 M)
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 non-linear 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
آمار
تعداد مشاهده مقاله: 142
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