High Order IMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings

In this paper,we consider the high order method for solving the linear transport equations under diffusive scaling and with random inputs.To tackle the randomness in the problem,the stochastic Galerkin method of the generalized polynomial chaos approach has been employed.Besides,the high order implicit-explicit scheme under the micro-macro decomposition framework and the discontinuous Galerkin method have been employed.We provide several numerical experiments to validate the accuracy and the stochastic asymptotic-preserving property.

Lagrangian statistics in isotropic turbulent flows with deterministic and stochastic forcing schemes

Artificial input of energy into the flow is neces sary to create and maintain a statistically stationary isotropic turbulence for sampling in studying the statistics. Due to the nonlinear coupling among different Fourier modes through the triadic interaction, whether or not various forc ing schemes affect the statistics in turbulence is an impor tant and open question. We present detailed comparison of Lagrangian statistics of fluids particles in forced isotropic turbulent flows in 1283, 2563, and 5123 simulations, with Taylorscale Reynolds numbers in the range of 64-171, us ing a deterministic and a stochastic forcing scheme, respec tively. Several Lagrangian statistics are compared, such as velocity and acceleration autocorrelations, and moments of Lagrangian velocity increments. The differences in the La grangian statistics obtained from the two forcing schemes are shown to be small, indicating that the isotropic forcing schemes used have little effects on the Lagrangian statistics in the isotropic turbulence.

A Reliable Stochastic Numerical Analysis for Typhoid Fever Incorporating With Protection Against Infection

In this paper,a reliable stochastic numerical analysis for typhoid fever incorporating with protection against infection has been considered.We have compared the solutions of stochastic and deterministic typhoid fever model.It has been shown that the stochastic typhoid fever model is more realistic as compared to the deterministic typhoid fever model.The effect of threshold number T*hold in stochastic typhoid fever model.The proposed framework of the stochastic non-standard finite difference scheme(SNSFD)preserves all dynamical properties like positivity,bounded-ness and dynamical consistency defined by Mickens,R.E.The stochastic numerical simulation of the model showed that increase in protection leads to low disease prevalence in a population.

TWO-STEP SCHEME FOR BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS

In this paper,a stochastic linear two-step scheme has been presented to approximate backward stochastic differential equations(BSDEs).A necessary and sufficient condition is given to judge the L 2-stability of our numerical schemes.This stochastic linear two-step method possesses a family of 3-order convergence schemes in the sense of strong stability.The coefficients in the numerical methods are inferred based on the constraints of strong stability and n-order accuracy(n∈N^(+)).Numerical experiments illustrate that the scheme is an efficient probabilistic numerical method.