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A Chebyshev collocation based sequential matrix exponential method for the generalized density evolution equation
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DOI：10.1016/j.probengmech.2021.103118.png)
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In perspective of global approximation, this study presents a numerical method for the generalized density evolution equation (GDEE) based on spectral collocation. A sequential matrix exponential solution based on the Chebyshev collocation points is derived in consideration of the coefficient or velocity term of GDEE being constant in each time step, then the numerical procedure could be successively implemented without implicit or explicit difference schemes. The results of three numerical examples indicate that the solutions in terms of the sequential matrix exponential method for GDEE have good agreement with the analytical results or Monte Carlo simulations. For sufficiently smooth cases, there need no more than one hundred representative points to achieve a satisfied solution by the proposed method, whereas for the case in presence of severe discontinuity a few more sampling points are required to keep numerical stability and accuracy.
Keyword:
Probability density evolution method
Spectral method
Chebyshev polynomial
Collocation
Matrix exponential
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A note on the principle of preservation of probability and probability density evolution equation关于概率和概率密度演化方程保存原理的注记
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