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Interval Wavelet Numerical Method on Fokker‐Planck Equations for Nonlinear Random System

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  • Li-wei Liu

Abstract

The Fokker‐Planck‐Kolmogorov (FPK) equation governs the probability density function (p.d.f.) of the dynamic response of a particular class of linear or nonlinear system to random excitation. An interval wavelet numerical method (IWNM) for nonlinear random systems is proposed using interval Shannon‐Gabor wavelet interpolation operator. An FPK equation for nonlinear oscillators and a time fractional Fokker‐Planck equation are taken as examples to illustrate its effectiveness and efficiency. Compared with the common wavelet collocation methods, IWNM can decrease the boundary effect greatly. Compared with the finite difference method for the time fractional Fokker‐Planck equation, IWNM can improve the calculation precision evidently.

Suggested Citation

  • Li-wei Liu, 2013. "Interval Wavelet Numerical Method on Fokker‐Planck Equations for Nonlinear Random System," Advances in Mathematical Physics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlamp:v:2013:y:2013:i:1:n:651357
    DOI: 10.1155/2013/651357
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    References listed on IDEAS

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    1. Shu-Li Mei, 2013. "HAM‐Based Adaptive Multiscale Meshless Method for Burgers Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
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    7. Shu-Li Mei, 2013. "Construction of Target Controllable Image Segmentation Model Based on Homotopy Perturbation Technology," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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    1. Ruyi Xing & Meng Liu & Kexin Meng & Shuli Mei, 2021. "Coupling Technique of Haar Wavelet Transform and Variational Iteration Method for a Nonlinear Option Pricing Model," Mathematics, MDPI, vol. 9(14), pages 1-15, July.

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