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| Numerical computation of differential dynamic systems using boundary value methods |
| Received:November 07, 2016 Revised:May 05, 2017 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx201706007 |
| KeyWord:dynamic systems boundary value methods differential quadrature methods generalized backward differentiation formulae extended trapezoidal rules |
| Author | Institution |
| 汪芳宗 |
三峡大学 电气与新能源学院, 宜昌 |
| 潘明帅 |
三峡大学 电气与新能源学院, 宜昌 |
| 杨萌 |
三峡大学 电气与新能源学院, 宜昌 |
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| Abstract: |
| For the high dimensional nonlinear initial value problem,the differential quadrature method(DQM) can be used to solve a higher dimensional nonlinear equations in the integration process of each step,so its computation workload is huge.Based on the relationship between DQM and the boundary value methods,the generalized backward difference formulae(GBDF) and the extended implicit trapezoidal rules of the second kind(ETR2) can be regarded as the sparse representation of classical DQM.In this paper,the GBDF methods and ETR2 are applied to the numerical solution of the differential dynamic systems,and a new numerical method is proposed.Theoretical analysis and numerical examples show that,the proposed numerical method has higher computational efficiency than classical DQM for the numerical solution of the nonlinear differential initial value problem with high dimensions. |