Abstract We study the multiplicative version of classical Furstenberg’s filtering problem, where instead sum $$\textbf{X}+\textbf{Y}$$ X+Y one considers product $$\textbf{X}\cdot \textbf{Y}$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">...

This paper is concerned with finding numerical solutions of a flow of ODE solutions. It describes a new method, based on Euler Backward method and interpolation, for finding solutions of autonomous problems. The special aspect is that this method is explicit, and resolves the flow with similar accuracy as Euler Backward method, even when the problem is stiff. An analysis is given of both stabil...

For uncertain differential equations, we cannot always obtain their analytic solutions. Early researchers have described the Euler method and Runge–Kutta method for solving uncertain differential equations. This paper proposes a new numerical method—Adams method to solve uncertain differential equations. Some numerical experiments are given to illustrate the efficiency of our numerical method. ...

This paper presents a multiscale simulation method for self-organization of nanoparticles in a dense suspension. The method consists of a solid–liquid two-phase model, in which the flow of solvent and the motion of nanoparticles are treated by an Euler–Lagrange hybrid scheme with a dual time stepping. The method also includes various multiscale forces whose characteristic length and time scales...

In this paper, an adaptive approach based on a time discontinuous Galerkin method (dG) is proposed. For large time steps and in a linear non-autonomous case, it reduces to the asymptotically second-order accurate Lobatto IIIC type implicit Runge-Kutta method, which is equal to the Padé-(0,2) approximation of the exponential function. In the asymptotic range it will result in the asymptotically ...

Adaptive solution techniques are presented for simulating underwater explosions and implosions. The liquid is assumed to be an adiabatic fluid and the solution in the gas is assumed to be uniform in space. The solution in the water is integrated in time using a semi-implicit time discretization of the adiabatic Euler equations. Results are presented either using a non-conservative semi-implicit...