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An Advanced Numerical Approach for Solving Stiff Initial Value Problems Using a Self-Starting Two-Stage Composite Block Scheme | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 12 اردیبهشت 1404 اصل مقاله (1.4 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.65372.3001 | ||
| نویسندگان | ||
| Badrul Amin Jaafar؛ Iskandar Shah Mohd Zawawi* | ||
| Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia. | ||
| چکیده | ||
| In this study, a two-point composite block method based on the backward differentiation formula (CBBDF) is introduced to solve stiff ordinary differential equations. The CBBDF method incorporates an additional intermediate point among the interpolating points, developed in two stages: the first stage employs the Euler’s method as a fundamental building block, while the second stage utilizes CBBDF of order three. A key distinction of the method with the classical block method is the introduction of an independent parameter γ, which eliminates the need for an external startup calculation, while maintaining the accuracy and stability of numerical solutions. The theoretical analysis verifies that the proposed method is convergent and A-stable. It fulfills the essential properties of consistency and zero-stability, and it lies within the A-stability region. To demonstrate the effectiveness of the proposed approach, several stiff initial value problems of linear and non-linear are solved. For validation, the results are compared with existing literature. While approximating the solution at multiple points simultaneously, the composite block method offers the ability to use larger step sizes for solution approximation. The CBBDF method shows promising results, achieving a reliable degree of accuracy as indicated by its maximum error and average error measurements. | ||
| کلیدواژهها | ||
| backward differentiation formula؛ block method؛ composite scheme؛ linear multi-sub-step method؛ stiff differential equations | ||
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آمار تعداد مشاهده مقاله: 192 تعداد دریافت فایل اصل مقاله: 234 |
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