Monte-Carlo simulation of a stochastic differential equation

Arif ULLAH; Majid KHAN; M KAMRAN; R KHAN; Zhengmao SHENG (盛正卯)

doi:10.1088/2058-6272/aa8f3f

Plasma Science and Technology > 2017 > 19(12): 125001. > DOI: 10.1088/2058-6272/aa8f3f

Arif ULLAH, Majid KHAN, M KAMRAN, R KHAN, Zhengmao SHENG (盛正卯). Monte-Carlo simulation of a stochastic differential equation[J]. Plasma Science and Technology, 2017, 19(12): 125001. DOI: 10.1088/2058-6272/aa8f3f

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Monte-Carlo simulation of a stochastic differential equation

1 Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, People’s Republic of China 2 Department of Physics Quaid-i-Azam University Islamabad, Pakistan 3 Department of Physics, Institute of Fusion Theory and Simulations, Zhejiang University, Hangzhou 310027, People’s Republic of China 4 Department of Physics, COMSATS Institute of Information Technology, Chack Shahzad, Islamabad, Pakistan 5 Department of Physics, Abdul Wali Khan University, 23200 Mardan, KPK, Pakistan

Funds: This publication is based on the research that has been supported in part by the Higher Education Commission of Pakistan under PPCR program. As well as this, work was supported by the National Magnetic Confinement Fusion Program under Grant No. 2013GB104004 and Fundamental Research Fund for Chinese Central Universities.

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Received Date: May 23, 2017

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Abstract

Abstract

For solving higher dimensional diffusion equations with an inhomogeneous diffusion coefficient, Monte Carlo (MC) techniques are considered to be more effective than other algorithms, such as finite element method or finite difference method. The inhomogeneity of diffusion coefficient strongly limits the use of different numerical techniques. For better convergence, methods with higher orders have been kept forward to allow MC codes with large step size. The main focus of this work is to look for operators that can produce converging results for large step sizes. As a first step, our comparative analysis has been applied to a general stochastic problem. Subsequently, our formulization is applied to the problem of pitch angle scattering resulting from Coulomb collisions of charge particles in the toroidal devices.
- Monte-Carlo simulation,
- stochastic differential equations,
- toroidal plasmas,
- numerical methods

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References (37)

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