计算力学学报2017，Vol.34Issue(6)：718-724,7.DOI:10.7511/jslx201706007
基于边界值方法的微分动力系统数值计算方法
Numerical computation of differential dynamic systems using boundary value methods
摘要
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.关键词
动力系统/边界值方法/微分求积法/广义向后差分方法/扩展的隐式梯形积分方法Key words
dynamic systems/boundary value methods/differential quadrature methods/generalized backward differentiation formulae/extended trapezoidal rules分类
数理科学引用本文复制引用
汪芳宗,潘明帅,杨萌..基于边界值方法的微分动力系统数值计算方法[J].计算力学学报,2017,34(6):718-724,7.基金项目
国家自然科学基金(51377098)资助项目. （51377098）
