Fast and Accurate Numerical Integration of the Langevin Equation with Multiplicative Gaussian White Noise
A univariate stochastic system driven by multiplicative Gaussian white noise is considered. The standard method for simulating its Langevin equation of motion involves incrementing the system’s state variable by a biased Gaussian random number at each time step. It is shown that the efficiency of su...
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2024-10-01
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| author | Mykhaylo Evstigneev Deniz Kacmazer |
| author_facet | Mykhaylo Evstigneev Deniz Kacmazer |
| author_sort | Mykhaylo Evstigneev |
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| description | A univariate stochastic system driven by multiplicative Gaussian white noise is considered. The standard method for simulating its Langevin equation of motion involves incrementing the system’s state variable by a biased Gaussian random number at each time step. It is shown that the efficiency of such simulations can be significantly enhanced by incorporating the skewness of the distribution of the updated state variable. A new algorithm based on this principle is introduced, and its superior performance is demonstrated using a model of free diffusion of a Brownian particle with a friction coefficient that decreases exponentially with the kinetic energy. The proposed simulation technique proves to be accurate over time steps that are an order of magnitude longer than those required by standard algorithms. The model used to test the new numerical technique is known to exhibit a transition from normal diffusion to superdiffusion as the environmental temperature rises above a certain critical value. A simple empirical formula for the time-dependent diffusion coefficient, which covers both diffusion regimes, is introduced, and its accuracy is confirmed through comparison with the simulation results. |
| format | Article |
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| institution | OA Journals |
| issn | 1099-4300 |
| language | English |
| publishDate | 2024-10-01 |
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| series | Entropy |
| spelling | doaj-art-6e4a9a14b24c4e048af13baac5b9cf472025-08-20T02:11:09ZengMDPI AGEntropy1099-43002024-10-01261087910.3390/e26100879Fast and Accurate Numerical Integration of the Langevin Equation with Multiplicative Gaussian White NoiseMykhaylo Evstigneev0Deniz Kacmazer1Department of Physics and Physical Oceanography, Memorial University of Newfoundland, St. John’s, NL A1B 3X7, CanadaDepartment of Physics and Physical Oceanography, Memorial University of Newfoundland, St. John’s, NL A1B 3X7, CanadaA univariate stochastic system driven by multiplicative Gaussian white noise is considered. The standard method for simulating its Langevin equation of motion involves incrementing the system’s state variable by a biased Gaussian random number at each time step. It is shown that the efficiency of such simulations can be significantly enhanced by incorporating the skewness of the distribution of the updated state variable. A new algorithm based on this principle is introduced, and its superior performance is demonstrated using a model of free diffusion of a Brownian particle with a friction coefficient that decreases exponentially with the kinetic energy. The proposed simulation technique proves to be accurate over time steps that are an order of magnitude longer than those required by standard algorithms. The model used to test the new numerical technique is known to exhibit a transition from normal diffusion to superdiffusion as the environmental temperature rises above a certain critical value. A simple empirical formula for the time-dependent diffusion coefficient, which covers both diffusion regimes, is introduced, and its accuracy is confirmed through comparison with the simulation results.https://www.mdpi.com/1099-4300/26/10/879Langevin equationmultiplicative noisediffusioncomputational physics |
| spellingShingle | Mykhaylo Evstigneev Deniz Kacmazer Fast and Accurate Numerical Integration of the Langevin Equation with Multiplicative Gaussian White Noise Entropy Langevin equation multiplicative noise diffusion computational physics |
| title | Fast and Accurate Numerical Integration of the Langevin Equation with Multiplicative Gaussian White Noise |
| title_full | Fast and Accurate Numerical Integration of the Langevin Equation with Multiplicative Gaussian White Noise |
| title_fullStr | Fast and Accurate Numerical Integration of the Langevin Equation with Multiplicative Gaussian White Noise |
| title_full_unstemmed | Fast and Accurate Numerical Integration of the Langevin Equation with Multiplicative Gaussian White Noise |
| title_short | Fast and Accurate Numerical Integration of the Langevin Equation with Multiplicative Gaussian White Noise |
| title_sort | fast and accurate numerical integration of the langevin equation with multiplicative gaussian white noise |
| topic | Langevin equation multiplicative noise diffusion computational physics |
| url | https://www.mdpi.com/1099-4300/26/10/879 |
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