In this paper we present a type of asymptotic integration for a certain scalar time\|varying functional differential equations with L\+p\|integrable coefficients. The main theorem we obtain generalizes the result of H...In this paper we present a type of asymptotic integration for a certain scalar time\|varying functional differential equations with L\+p\|integrable coefficients. The main theorem we obtain generalizes the result of Haddock & Sacker′s Conjecture with n=1.展开更多
Applying Laplace asymptotic approximation of integral, asymptotic analysis methods of structural reliability are proposed in generalized and orthogonal random space. Analytic results show that the proposed methods are...Applying Laplace asymptotic approximation of integral, asymptotic analysis methods of structural reliability are proposed in generalized and orthogonal random space. Analytic results show that the proposed methods are simple in calculation and accurate enough for problems of continuous random variables.展开更多
While the numerical solution of one-dimensional Volterra integral equations of the second kind with regular kernels is well understood, there exist no systematic studies of asymptotic error expansion for the approxima...While the numerical solution of one-dimensional Volterra integral equations of the second kind with regular kernels is well understood, there exist no systematic studies of asymptotic error expansion for the approximate solution. In this paper,we analyse the Nystrom solution of one-dimensional nonlinear Volterra integral equation of the second kind and show that approkimate solution admits an asymptotic error expansion in even powers of the step-size h, beginning with a term in h2. So that the Richardson's extrapolation can be done. This will increase the accuracy of numerical solution greatly.展开更多
文摘In this paper we present a type of asymptotic integration for a certain scalar time\|varying functional differential equations with L\+p\|integrable coefficients. The main theorem we obtain generalizes the result of Haddock & Sacker′s Conjecture with n=1.
文摘Applying Laplace asymptotic approximation of integral, asymptotic analysis methods of structural reliability are proposed in generalized and orthogonal random space. Analytic results show that the proposed methods are simple in calculation and accurate enough for problems of continuous random variables.
文摘While the numerical solution of one-dimensional Volterra integral equations of the second kind with regular kernels is well understood, there exist no systematic studies of asymptotic error expansion for the approximate solution. In this paper,we analyse the Nystrom solution of one-dimensional nonlinear Volterra integral equation of the second kind and show that approkimate solution admits an asymptotic error expansion in even powers of the step-size h, beginning with a term in h2. So that the Richardson's extrapolation can be done. This will increase the accuracy of numerical solution greatly.
