In this paper, we discuss local convergence of a family of Chebychev Halley type methods with a parameter θ∈[0,1] in Banach space using Smale type δ criterion under 2 th γ condition. We will see that the propertie...In this paper, we discuss local convergence of a family of Chebychev Halley type methods with a parameter θ∈[0,1] in Banach space using Smale type δ criterion under 2 th γ condition. We will see that the properties of the condition used for local convergence is much more different from that used in [6][15] for the semi-local convergence.展开更多
An annular sector model for the telephone cord buckles of elastic thin films on rigid substrates is established, in which the von Krman plate equations in polar coordinates are used for the elastic thin film and a dis...An annular sector model for the telephone cord buckles of elastic thin films on rigid substrates is established, in which the von Krman plate equations in polar coordinates are used for the elastic thin film and a discrete version of the Griffith criterion is applied to determine the shape and scale of the parameters. A numerical algorithm combining the Newmark-β scheme and the Chebyshev collocation method is designed to numerically solve the problem in a quasi-dynamic process. Numerical results are presented to show that the numerical method works well and the model agrees well with physical observations, especially successfully simulated for the first time the telephone cord buckles with two humps along the ridge of each section of a buckle.展开更多
文摘In this paper, we discuss local convergence of a family of Chebychev Halley type methods with a parameter θ∈[0,1] in Banach space using Smale type δ criterion under 2 th γ condition. We will see that the properties of the condition used for local convergence is much more different from that used in [6][15] for the semi-local convergence.
基金supported by the Major State Basic Research Projects (Grant No. 2005CB321701)National Natural Science Foundation of China (Grant No. 10871011)Research Foundation of Doctoral Program of the Ministry of Education of China (Grant No. 20060001007)
文摘An annular sector model for the telephone cord buckles of elastic thin films on rigid substrates is established, in which the von Krman plate equations in polar coordinates are used for the elastic thin film and a discrete version of the Griffith criterion is applied to determine the shape and scale of the parameters. A numerical algorithm combining the Newmark-β scheme and the Chebyshev collocation method is designed to numerically solve the problem in a quasi-dynamic process. Numerical results are presented to show that the numerical method works well and the model agrees well with physical observations, especially successfully simulated for the first time the telephone cord buckles with two humps along the ridge of each section of a buckle.
