An Analog Equation Method-Based Numerical Scheme for Initial Value Problems of Stochastic Fractional Differential Equations

SUN Chun-yan; XU Wei

doi:10.3879/j.issn.1000-0887.2014.10.003

Volume 35 Issue 10

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SUN Chun-yan, XU Wei. An Analog Equation Method-Based Numerical Scheme for Initial Value Problems of Stochastic Fractional Differential Equations[J]. Applied Mathematics and Mechanics, 2014, 35(10): 1092-1099. doi: 10.3879/j.issn.1000-0887.2014.10.003

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An Analog Equation Method-Based Numerical Scheme for Initial Value Problems of Stochastic Fractional Differential Equations

doi: 10.3879/j.issn.1000-0887.2014.10.003

Department of Applied Mathematics, School of Natural and Applied Sciences, Northwestern Polytechnical University, Xi’an 710072, P.R.China

Funds: The National Natural Science Foundation of China（11772233）

Received Date: 2014-05-19
Rev Recd Date: 2014-09-08
Publish Date: 2014-10-15

Abstract

Abstract

An analog-equation-method (AEM)-based numerical scheme was proposed for initial value problems of stochastic fractional differential equations with 2 fractional derivative terms. 2 stochastic analog equations comprising respective undetermined functions were introduced, to convert the problem to a fractional differential equation with only 1 fractional derivative term. The Laplace transform and its inverse were employed to get the integration representations for the solution to the fractional differential equation and establish the relation between the 2 analog equations. In view of the initial conditions, an iterative algorithm to solve the initial value problem of the stochastic fractional differential equation was obtained. In a typical case, the numerical solution to a linear stochastic ordinary differential equation with 2 fractional derivative terms was derived based on the AEM. The numerical results of both the definite and stochastic systems demonstrate the effectiveness, stability and accuracy of the presented AEM scheme, of which the error only lies in the truncation error of the integration approximation and the rounding error of the computation software.
- fractional derivative,
- stochastic fractional differential equation,
- analog equation,
- initial value problem

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References(25)

References

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