A novel extended precise integration method based on Fourier series expansion for periodic Riccati differential equations

2017 ◽  
Vol 38 (6) ◽  
pp. 896-907 ◽  
Author(s):  
Shu-Jun Tan ◽  
Wen-Ya Zhou ◽  
Hai-Jun Peng ◽  
Zhi-Gang Wu
Keyword(s):  
Fourier Series ◽  
Differential Equations ◽  
Series Expansion ◽  
Integration Method ◽  
Fourier Series Expansion ◽  
Precise Integration ◽  
Precise Integration Method ◽  
Riccati Differential Equations ◽  
Extended Precise Integration Method

scholarly journals Adaptive Wavelet Precise Integration Method for Nonlinear Black-Scholes Model Based on Variational Iteration Method

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Huahong Yan
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Iteration Method ◽  
Integration Method ◽  
Variational Iteration Method ◽  
Precise Integration ◽  
Adaptive Wavelet ◽  
Precise Integration Method ◽  
Black Scholes Model ◽  
Black Scholes

An adaptive wavelet precise integration method (WPIM) based on the variational iteration method (VIM) for Black-Scholes model is proposed. Black-Scholes model is a very useful tool on pricing options. First, an adaptive wavelet interpolation operator is constructed which can transform the nonlinear partial differential equations into a matrix ordinary differential equations. Next, VIM is developed to solve the nonlinear matrix differential equation, which is a new asymptotic analytical method for the nonlinear differential equations. Third, an adaptive precise integration method (PIM) for the system of ordinary differential equations is constructed, with which the almost exact numerical solution can be obtained. At last, the famous Black-Scholes model is taken as an example to test this new method. The numerical result shows the method's higher numerical stability and precision.

Instability Analysis of Parametrically Excited Marine Risers by Extended Precise Integration Method

2017 ◽  
Vol 17 (08) ◽  
pp. 1750096 ◽  
Author(s):  
Song Lei ◽  
Xiang Yuan Zheng ◽  
Daoyi Chen ◽  
Yi Li
Keyword(s):  
Integration Method ◽  
Dynamic Instability ◽  
Lateral Displacement ◽  
Dynamic Buckling ◽  
Structural Safety ◽  
Local Dynamic ◽  
Precise Integration ◽  
Precise Integration Method ◽  
Hydrodynamic Damping ◽  
Extended Precise Integration Method

The objective of this paper is to investigate the dynamic instability of deepwater top-tensioned risers (TTRs), when subjected to the fluctuating axial tension originated from the heave motion of a surface floating platform as the instability source. Based on a rigorous derivation on the governing equation, a reduced model of the lateral displacement of a TTR is achieved by an ordinary differential equation with periodic coefficients. To identify the instability range of practical amplitudes and frequencies of the excitation, a newly proposed extended precise integration method (EPIM) is employed to generate the Floquet transition matrix (FTM). EPIM possesses high precision and efficiency due to the doubling algorithm and the increment-storing technique. The instability charts of TTRs in several typical depths are numerically obtained using EPIM. The effects of factors such as the top tension ratio, the stiffness of the heave compensators, damping constant, and internal flow velocity on the instability region are analyzed. In addition, because the nonlinear hydrodynamic damping will lead the TTR’s lateral vibration to reach a steady state, the instability response is thereby simulated by EPIM. Three response scenarios are discussed with examples. As the heave amplitude increases, the parametric resonance of the TTR is first triggered, then the transition stage appears, and ultimately the local dynamic buckling occurs. The bending stress analysis shows that the local dynamic buckling is the worst scenario for structural safety.

scholarly journals Shannon-Cosine Wavelet Precise Integration Method for Locust Slice Image Mixed Denoising

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Haihua Wang ◽  
Xinxin Zhang ◽  
Shuli Mei
Keyword(s):  
Wavelet Transform ◽  
Differential Equations ◽  
Sparse Representation ◽  
Integration Method ◽  
Nonlinear Differential Equations ◽  
Variational Model ◽  
Precise Integration ◽  
Edge Preserving ◽  
Precise Integration Method ◽  
Salt And Pepper

A novel denoising method for removing mixed noise from locust slice images is proposed by means of Shannon-cosine wavelet and the nonlinear variational model for the image processing. This method includes two parts that are the sparse representation of the slice images and the novel numerical algorithm for solving the variation model on image denoising based on the sparse representation. In the first part, a parametric Shannon-cosine wavelet function is introduced to construct the multiscale wavelet transform matrix, which is applied to represent the slice images sparsely by adjusting the parameters adaptively based on the texture of the locust slice images. By multiplying the matrix with the signal, the multiscale wavelet transform coefficients of the signal can be obtained at one time, which can be used to identify the salt-and-pepper noises in the slice images. This ensures that the salt-and-pepper noise points are kept away from the sparse representation of the slice images. In the second part, a semianalytical method on solving the system of the nonlinear differential equations is constructed based on the sparse representation of the slice images, which is named the sparse wavelet precise integration method (SWPIM). Substituting the sparse representation of the slice images into the Perona–Malik model which is the famous edge-preserving smoothing model for removing the Gaussian noises of the biomedical images, a system of nonlinear differential equations is obtained, whose scale is far smaller than the one obtained by the difference method. The numerical experiments show that both the values of SSIM and PSNR of the denoised locust slice images are better than the classical methods besides the algorithm efficiency.

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