A class of third-order convergence methods of solving roots for non-linear equation,which are variant Newton＇s method, are given. Their convergence properties are proved. They are at least third order convergence nea...A class of third-order convergence methods of solving roots for non-linear equation,which are variant Newton＇s method, are given. Their convergence properties are proved. They are at least third order convergence near simple root and one order convergence near multiple roots. In the end, numerical tests are given and compared with other known Newton＇s methods. The results show that the proposed methods have some more advantages than others. They enrich the methods to find the roots of non-linear equations and they are important in both theory and application.展开更多
The buckling design of micro-films has various potential applications to engineering.The substrate prestrain,interconnector buckling amplitude and critical strain are important parameters for the buckling design.In th...The buckling design of micro-films has various potential applications to engineering.The substrate prestrain,interconnector buckling amplitude and critical strain are important parameters for the buckling design.In the presented analysis,the buckled film shape was described approximately by a trigonometric function and the buckled film amplitude was obtained by minimizing the total strain energy.However,this method only generates the first-order approximate solution for the nonlinear buckling.In the present paper,an asymptotic analysis based on the rigorous nonlinear differential equation for the buckled micro-film deformations is proposed to obtain more accurate relationship of the buckling amplitude and critical strain to prestrain.The obtained results reveal the nonlinear relation and are significant to accurate buckling design of micro-films.展开更多
基金Foundation item： Supported by the National Science Foundation of China（10701066）
文摘A class of third-order convergence methods of solving roots for non-linear equation,which are variant Newton＇s method, are given. Their convergence properties are proved. They are at least third order convergence near simple root and one order convergence near multiple roots. In the end, numerical tests are given and compared with other known Newton＇s methods. The results show that the proposed methods have some more advantages than others. They enrich the methods to find the roots of non-linear equations and they are important in both theory and application.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11002077 and 11072215)
文摘The buckling design of micro-films has various potential applications to engineering.The substrate prestrain,interconnector buckling amplitude and critical strain are important parameters for the buckling design.In the presented analysis,the buckled film shape was described approximately by a trigonometric function and the buckled film amplitude was obtained by minimizing the total strain energy.However,this method only generates the first-order approximate solution for the nonlinear buckling.In the present paper,an asymptotic analysis based on the rigorous nonlinear differential equation for the buckled micro-film deformations is proposed to obtain more accurate relationship of the buckling amplitude and critical strain to prestrain.The obtained results reveal the nonlinear relation and are significant to accurate buckling design of micro-films.
