Convergence Analysis of Implicit Euler Method for a Class of Nonlinear Impulsive Fractional Differential Equations

For a class of nonlinear impulsive fractional differential equations, we first transform them into equivalent integral equations, and then the implicit Euler method is adapted for solving the problem. The convergence analysis of the method shows that the method is convergent of the first order. The numerical results verify the correctness of the theoretical results.

NUMERICAL SIMULATION OF STOCHASTIC DIFFERENTIAL EQUATIONS USING IMPLICIT MILSTEIN METHOD

Stiff stochastic differential equations arise in many applications including in the area of biology. In this paper, we present numerical solution of stochastic differential equations representing the Malthus population model and SIS epidemic model, using the improved implicit Milstein method of order one proposed in [6]. The open source programming language SCILAB is used to perform the numerical simulations. Results show that the method is more accurate and stable compared to the implicit Euler method.

Nonlinear dynamic analysis of worn oil-lubricated rolling bearings

Based on the elastohydrodynamic theory, the nonlinear dynamic behavior of worn oil-lubricated rolling bearings is explored, and the dynamic response including the effect of trajectory of the axis center, the accelerated speed, and the film thickness is analyzed. The worn model is represented by the worn depth. The discrete iterative method and implicit Euler method are combined to solve the dynamic equations. In numerical examples, the trajectory of the axis center, the accelerated speed and the film thickness under different worn depths are discussed. It is found that the stabilized point shows significant variation with the worn depth, and the wear effect is also quite related with the rolling speed. The trajectory of the axis center of worn bearing subjected to a step load is also examined in detail.