Compensated split-step balanced methods for nonlinear stiff SDEs with jump-diffusion and piecewise continuous arguments

2020 ◽  
Vol 63 (12) ◽  
pp. 2573-2594
Author(s):  
Ying Xie ◽  
Chengjian Zhang
Keyword(s):  
Jump Diffusion ◽  
Piecewise Continuous ◽  
Piecewise Continuous Arguments

scholarly journals Numerical Solutions of Stochastic Differential Equations with Piecewise Continuous Arguments under Khasminskii-Type Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Minghui Song ◽  
Ling Zhang
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Growth Condition ◽  
Linear Growth ◽  
Numerical Solutions ◽  
Type Theorem ◽  
Global Existence Of Solutions ◽  
Linear Growth Condition ◽  
Piecewise Continuous ◽  
Piecewise Continuous Arguments

The main purpose of this paper is to investigate the convergence of the Euler method to stochastic differential equations with piecewise continuous arguments (SEPCAs). The classical Khasminskii-type theorem gives a powerful tool to examine the global existence of solutions for stochastic differential equations (SDEs) without the linear growth condition by the use of the Lyapunov functions. However, there is no such result for SEPCAs. Firstly, this paper shows SEPCAs which have nonexplosion global solutions under local Lipschitz condition without the linear growth condition. Then the convergence in probability of numerical solutions to SEPCAs under the same conditions is established. Finally, an example is provided to illustrate our theory.

SYMMETRIC BIFURCATIONS IN A RING OF COUPLED DIFFERENTIAL EQUATION WITH PIECEWISE CONTINUOUS ARGUMENTS

2011 ◽  
Vol 21 (02) ◽  
pp. 431-436 ◽  
Author(s):  
BAODONG ZHENG ◽  
JIAN MA ◽  
HUIFENG ZHENG ◽  
CHUNRUI ZHANG
Keyword(s):  
Differential Equation ◽  
Dihedral Group ◽  
Equilibrium Points ◽  
Piecewise Continuous ◽  
Piecewise Continuous Arguments ◽  
Group D

Symmetry bifurcations of equilibrium points of three coupled differential equation with piecewise continuous arguments (EPCA) oscillators are studied. The system is equivariant under dihedral group D3 with order 6. This causes several types of symmetrical bifurcations.

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