In this paper, we shall give an Abel type theorem of Jacobi series and then based on it discuss asymptotic expressions near the ellipse of convergence of Jacobi series in complex plane.
In this paper we consider the asymptotic expression of the solution of the Cauchy’sproblem for a higher order equation when the limit equation has singularity. In orderto construct the asymptotic expression of the so...In this paper we consider the asymptotic expression of the solution of the Cauchy’sproblem for a higher order equation when the limit equation has singularity. In orderto construct the asymptotic expression of the solution, the region is divided into threesub-areas. In every small region, the solution of the differential equation is different.展开更多
How to evaluate time-domain Green function and its gradients efficiently is the key problem to analyze ship hydrodynamics in time domain. Based on the Bessel function, an Ordinary Differential Equation （ODE） was der...How to evaluate time-domain Green function and its gradients efficiently is the key problem to analyze ship hydrodynamics in time domain. Based on the Bessel function, an Ordinary Differential Equation （ODE） was derived for time-domain Green function and its gradients in this paper. A new efficient calculation method based on solving ODE is proposed. It has been demonstrated by the numerical calculation that this method can improve the precision of the time-domain Green function. Numeiical research indicates that it is efficient to solve the hydrodynamic problems.展开更多
This paper deals with the steady-state bifurcation of the Kuramoto-Sivashinsky equation in one space dimension with periodic botmdary condition and of zero mean. The asymptotic expressions of the steady-state solution...This paper deals with the steady-state bifurcation of the Kuramoto-Sivashinsky equation in one space dimension with periodic botmdary condition and of zero mean. The asymptotic expressions of the steady-state solutions biftlrcated from the trivial solution are given. Furthermore, the stability of the nontrivial solutions are discussced.展开更多
文摘In this paper, we shall give an Abel type theorem of Jacobi series and then based on it discuss asymptotic expressions near the ellipse of convergence of Jacobi series in complex plane.
文摘In this paper we consider the asymptotic expression of the solution of the Cauchy’sproblem for a higher order equation when the limit equation has singularity. In orderto construct the asymptotic expression of the solution, the region is divided into threesub-areas. In every small region, the solution of the differential equation is different.
基金This work was financially supported by Key Program of the National Natural Science Foundation of China(No.50639020)the National High Technology Research and Development Program of China(863Program)(No.2006AA09Z332)
文摘How to evaluate time-domain Green function and its gradients efficiently is the key problem to analyze ship hydrodynamics in time domain. Based on the Bessel function, an Ordinary Differential Equation （ODE） was derived for time-domain Green function and its gradients in this paper. A new efficient calculation method based on solving ODE is proposed. It has been demonstrated by the numerical calculation that this method can improve the precision of the time-domain Green function. Numeiical research indicates that it is efficient to solve the hydrodynamic problems.
文摘This paper deals with the steady-state bifurcation of the Kuramoto-Sivashinsky equation in one space dimension with periodic botmdary condition and of zero mean. The asymptotic expressions of the steady-state solutions biftlrcated from the trivial solution are given. Furthermore, the stability of the nontrivial solutions are discussced.
