79 citations · 1k across the 43 of their papers we have counts for
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On the homotopy analysis method for backward/forward-backward stochastic differential equations
Xiaoxu Zhong, Shijun Liao
In this paper, an analytic approximation method for highly nonlinear equations, namely the homotopy analysis method (HAM), is employed to solve some backward stochastic differentia…
On the Generalized Wavelet-Galerkin Method
Zhaochen Yang, Shijun Liao
In the frame of the traditional wavelet-Galerkin method based on the compactly supported wavelets, it is important to calculate the so-called connection coefficients that are some…
On the origin of intrinsic randomness of Rayleigh-Benard turbulence
Zhiliang Lin, Lipo Wang, Shijun Liao
It is of broad interest to understand how the evolution of non-equilibrium systems can be triggered and the role played by external perturbations. A famous example is the origin of…
The influence of numerical noises on statistics computation of chaotic dynamic systems
Xiaoming Li, Shijun Liao
It is well known that chaotic dynamic systems (such as three-body system, turbulent flow and so on) have the sensitive dependance on initial conditions (SDIC). Unfortunately, numer…
Clean Numerical Simulation: A New Strategy to Obtain Reliable Solutions of Chaotic Dynamic Systems
Xiaoming Li, Shijun Liao
It is well known that chaotic dynamic systems (such as three-body system, turbulent flow and so on) have the sensitive dependence on initial conditions (SDIC). Unfortunately, numer…
Observation of two coupled Faraday waves in a vertically vibrating Hele-Shaw cell with one of them oscillating horizontally
Xiaochen Li, Xiaoming Li, Shijun Liao
A system of two-dimensional, two coupled Faraday interfacial waves is experimentally observed at the two interfaces of the three layers of fluids (air, pure ethanol and silicon oil…
Analytic Solutions of Von Karman Plate under Arbitrary Uniform Pressure (II): Equations in Integral Form
Xiaoxu Zhong, Shijun Liao
In this paper, the homotopy analysis method (HAM) is successfully applied to solve the Von Karman's plate equations in the integral form for a circular plate with the clamped bound…
Analytic Solutions of Von Karman Plate under Arbitrary Uniform Pressure --- Equations in Differential Form
Xiaoxu Zhong, Shijun Liao
The large deflection of a circular thin plate under uniform external pressure is a classic problem in solid mechanics, dated back to Von K{á}rm{á}n \cite{Karman}. {This problem is…