Rashidi, SaeedeHejazi, S. RezaMohammadizadeh, Fatemeh
30页
查看更多>>摘要：The topic of the present paper concentrates on a systematic investigation of Lie group analysis of non-linear time-fractional Black-Scholes equation including numerical approximations. Lie point symmetries of the equation are found via Riemann-Liouville derivative with four different volatility models. Also the invariant solutions as a kind of exact solutions are constructed by a useful explained method. Conservation laws for the intended equation are derived by using a modified version of Noether's theorem. A numerical simulation by Chebyshev pseudo-spectral (CPS) method is computed for the equation. Approximate solutions together with their absolute errors are found and the graphs of solutions are plotted by the action of order of derivative alpha. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we focus on the spectra numerical computation for the integral equation with the absolute oscillation and power-law or logarithmic singularity. Finite section method is applied to transform the integral equation to an algebraic eigenvalue problem. The entries of the coefficient matrix appearing in the bivariate highly oscillatory singular integrals can be represented explicitly in Gamma or the exponential integral functions. The decay rate of the entries is established to construct the truncation scheme. Then the infinite algebraic eigenvalue problem can be simplified to be the finite one. The corresponding error of the infinite and finite algebraic systems is also bounded. Finally, the numerical experiments are provided to illustrate the theoretical analysis. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In the current study, we provide a novel technique based on discrete shifted Hahn polynomials and Legendre-Gauss-Lobatto quadrature method for solving Caputo-Fabrizio fractional Volterra partial integro-differential equations (CFF-VPIDEs). The process of numerical algorithm contains the modified operational matrices (MOMs) and complement vectors (CVs), which directly influence the accuracy of the approach. Also, we expand the Volterra integral part of the equation with the help of the Legendre-Gauss- Lobatto quadrature method. The composition of the novel operational matrices with the Legendre-Gauss-Lobatto quadrature rule creates high precision and efficient method. Further, we present the error analysis of our scheme. Finally, to confirm the accuracy of theoretical results, we examine several examples. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：A family of varying-parameter finite-time zeroing neural networks (VPFTZNN) is introduced for solving the time-varying Sylvester equation (TVSE). The convergence speed of the proposed VPFTZNN family is analysed and compared with the traditional zeroing neural network (ZNN) and the finite-time zeroing neural network (FTZNN). The behaviour of the proposed neural networks under various activation functions is proved theoretically and verified experimentally. In addition, the stability and noise resistance of the proposed VPFTZNN family are discussed. Further, the proposed VPFTZNN models are applied in the computation of current flows in an electrical network. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we derive a class of equivariant estimators of the directional parameter of the Watson distribution with a known concentration parameter. When all parameters are unknown, we derive restricted maximum likelihood estimators (MLEs) of the concentration parameters and Bayes estimators of the parameters under a noninformative prior. An improved likelihood ratio test is proposed to test equality of directional parameters of several Watson distributions with a common concentration parameter. We derive rules to classify axial data into one of the Watson populations on the hypersphere when all parameters are unknown. We propose classification rules based on the MLEs and the Bayes estimators of the parameters. The likelihood ratio-based rule, predictive Bayes rule, and kernel density classifier have been derived for two Watson populations. Moreover, the rules are compared using simulations. (c) 2021 Elsevier B.V. All rights reserved.
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Elsevier