Numerical Simulation of Itô Stochastic Differential Equations on Supercomputers

1987 ◽  
pp. 215-228 ◽  
Author(s):  
W. P. Petersen
Keyword(s):  
Numerical Simulation ◽  
Differential Equations ◽  
Stochastic Differential Equations

scholarly journals NUMERICAL SIMULATION OF STOCHASTIC DIFFERENTIAL EQUATIONS USING IMPLICIT MILSTEIN METHOD

2020 ◽  
Vol 3 (1) ◽  
pp. 72-83
Author(s):  
Ratna Herdiana
Keyword(s):  
Numerical Simulation ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Programming Language ◽  
Population Model ◽  
Euler Method ◽  
Implicit Euler Method ◽  
Sis Epidemic Model ◽  
Milstein Method ◽  
Sis Epidemic

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.

Certain Problems with the Application of Stochastic Diffusion Processes for the Description of Chemical Engineering Phenomena. Numerical Simulation of One-Dimensional Diffusion Process

1996 ◽  
Vol 61 (4) ◽  
pp. 512-535 ◽  
Author(s):  
Pavel Hasal ◽  
Vladimír Kudrna
Keyword(s):  
Numerical Simulation ◽  
Diffusion Coefficient ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Chemical Engineering ◽  
Diffusion Processes ◽  
Stochastic Integral ◽  
Random Motion ◽  
One Dimensional ◽  
Dimensional Diffusion

Some problems are analyzed arising when a numerical simulation of a random motion of a large ensemble of diffusing particles is used to approximate the solution of a one-dimensional diffusion equation. The particle motion is described by means of a stochastic differential equation. The problems emerging especially when the diffusion coefficient is a function of spatial coordinate are discussed. The possibility of simulation of various kinds of stochastic integral is demonstrated. It is shown that the application of standard numerical procedures commonly adopted for ordinary differential equations may lead to erroneous results when used for solution of stochastic differential equations. General conclusions are verified by numerical solution of three stochastic differential equations with different forms of the diffusion coefficient.

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