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| Applications of Duhamel term’s precise integration method in solving nonlinear differential equations |
| Received:September 27, 2008 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20105002 |
| KeyWord:nonlinear Duhamel integration precise integration method Taylor series expanding Adams linear multi-step method stiffness |
| Author | Institution |
| 谭述君 |
大连理工大学 工业装备结构分析国家重点实验室,大连 |
| 高强 |
大连理工大学 工业装备结构分析国家重点实验室,大连 |
| 钟万勰 |
大连理工大学 工业装备结构分析国家重点实验室,大连 |
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| Abstract: |
| Several numerical algorithms for nonlinear differential equations are constructed based on Duhamel term’s precise integration method (PIM). Firstly the nonlinear differential equations are formally divided into linear and nonlinear parts and then the latter are approximated by polynomials. By applying the Duhamel integration, the general discrete forms for nonlinear differential equations are derived. Then the corresponding PIM-based algorithms are constructed by combining the traditional numerical integration techniques, such as Adams linear multi-step method, with PIM. Compared with the traditional algorithms, the new method integrates the linear part accurately by using PIM, and so improves the numerical precision and stability significantly, especially for stiff problems. Furthermore, the method proposed in this paper avoids the matrix inverse for the linear part and it is convenient to study effects of the linear matrix on the algorithm’s performance. Numerical experiments confirmed the validity of the proposed method and show that the linearization matrix of the nonlinear system is a good choice for the linear part. |
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