Based on protein-DNA complex crystal structural data in up-to-date Nucleic Acid Database,the related parameters of DNA Kinetic Structure were investigated by Monte-Carlo Multiple Integrals on the base of modified DNA ...Based on protein-DNA complex crystal structural data in up-to-date Nucleic Acid Database,the related parameters of DNA Kinetic Structure were investigated by Monte-Carlo Multiple Integrals on the base of modified DNA structure statistical mechanical model,and time complexity and precision were analyzed on the calculated results.展开更多
In this work, we consider the second order nonlinear integro-differential Equation (IDEs) of the Volterra-Fredholm type. One of the popular methods for solving Volterra or Fredholm type IDEs is the method of quadratur...In this work, we consider the second order nonlinear integro-differential Equation (IDEs) of the Volterra-Fredholm type. One of the popular methods for solving Volterra or Fredholm type IDEs is the method of quadrature while the problem of consideration is a linear problem. If IDEs are nonlinear or integral kernel is complicated, then quadrature rule is not most suitable;therefore, other types of methods are needed to develop. One of the suitable and effective method is homotopy analysis method (HAM) developed by Liao in 1992. To apply HAM, we firstly reduced the IDEs into nonlinear integral Equation (IEs) of Volterra-Fredholm type;then the standard HAM was applied. Gauss-Legendre quadrature formula was used for kernel integrations. Obtained system of algebraic equations was solved numerically. Moreover, numerical examples demonstrate the high accuracy of the proposed method. Comparisons with other methods are also provided. The results show that the proposed method is simple, effective and dominated other methods.展开更多
基金Supported by Inner Mongolia Natural Science Foundation(200711020112)Innovation Fundation of Inner Mongolia University of Science and Technology (2009NC064)~~
文摘Based on protein-DNA complex crystal structural data in up-to-date Nucleic Acid Database,the related parameters of DNA Kinetic Structure were investigated by Monte-Carlo Multiple Integrals on the base of modified DNA structure statistical mechanical model,and time complexity and precision were analyzed on the calculated results.
文摘In this work, we consider the second order nonlinear integro-differential Equation (IDEs) of the Volterra-Fredholm type. One of the popular methods for solving Volterra or Fredholm type IDEs is the method of quadrature while the problem of consideration is a linear problem. If IDEs are nonlinear or integral kernel is complicated, then quadrature rule is not most suitable;therefore, other types of methods are needed to develop. One of the suitable and effective method is homotopy analysis method (HAM) developed by Liao in 1992. To apply HAM, we firstly reduced the IDEs into nonlinear integral Equation (IEs) of Volterra-Fredholm type;then the standard HAM was applied. Gauss-Legendre quadrature formula was used for kernel integrations. Obtained system of algebraic equations was solved numerically. Moreover, numerical examples demonstrate the high accuracy of the proposed method. Comparisons with other methods are also provided. The results show that the proposed method is simple, effective and dominated other methods.
