In the present paper, a class of stochastic Runge–Kutta methods containing the second order stochastic Runge–Kutta scheme due to E. Platen for the weak approximation of Itô stochastic differential equation systems with a multi-dimensional Wiener process is considered. Order 1 and order 2...

We consider scalar stochastic differential equations of the formdXt=μ(Xt)dt+σ(Xt)dBt,X0=x0,where B is a standard Brownian motion. Suppose that the coefficients are such that the solution X possesses the (a, b)-invariance property for some interval (a,b)⊂R:Xt∈(a,b) for all t≥0 if...

The present analysis is an application of the continuous time replicator dynamic to economics. Three types of problems are considered under conditions of a normalized constraint and non-negative constrains. The story of the following models is as follows. There are three or more corporations in...

Rumor is an important form of social interaction, and its spreading has a significant impact on people’s lives. In the age of Web, people are using electronic media more frequently than ever before, and blog has become one of the main online social interactions. Therefore, it is essential to...

This paper deals with numerical solution of two-dimensional and three-dimensional steady and unsteady laminar incompressible flows for Newtonian and non-Newtonian shear thickening fluids flow through a branching channel. The mathematical model used in this work is the generalized system of...

This paper deals with the numerical solution of Newtonian and non-Newtonian flows with biomedical applications. The flows are supposed to be laminar, viscous, incompressible and steady or unsteady with prescribed pressure variation at the outlet. The model used for non-Newtonian fluids is a...

When simulating trajectories by integrating time-continuous car-following models, standard integration schemes such as the fourth-order Runge–Kutta method (RK4) are rarely used while the simple Euler method is popular among researchers. We compare four explicit methods both analytically and...

We propose two new positive weak second-order approximations for the CIR equation dXt=(a−bXt)dt+σXtdBt based on splitting, at each step, the equation into the deterministic part dXt=(a−bXt)dt, which is solved exactly, and the stochastic part dXt=σXtdBt, which is approximated in...

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