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Numerical Solutions of Fractional Variable Order Differential Equations via Using shifted legendre polynomials

Computer Modeling in Engineering & Sciences 2023年第2期134卷 941-955页

作者： Kamal Shah Hafsa Naz Thabet Abdeljawad Aziz Khan Manar A.Alqudah Department of Mathematics and Sciences Prince Sultan UniversityRiyadh11586Saudi Arabia Department of Mathematics University of MalakandChakdara Dir(L)Khyber Pakhtunkhwa18000Pakistan Department of Medical Research China Medical UniversityTaichung40402Taiwan Department of Mathematical Sciences Faculty of SciencesPrincess Nourah bint Abdurahman UniversityRiyadh11671Saudi Arabia

In this manuscript,an algorithm for the computation of numerical solutions to some variable order fractional differential equations(FDEs)subject to the boundary and initial conditions is *** use shifted legendre polynomials for the required numerical algorithm to develop some operational ***,operational matrices are constructed using variable order differentiation and *** are finding the operationalmatrices of variable order differentiation and integration by omitting the discretization of *** the help of aforesaid matrices,considered FDEs are converted to algebraic equations of Sylvester ***,the algebraic equations we get are solved with the help of mathematical software like Matlab or Mathematica to compute numerical *** examples are given to check the proposed method’s accuracy and graphical *** and numerical solutions are also compared in the paper for some *** efficiency of the method can be enhanced further by increasing the scale level.

关键词： Operational matrices shifted legendre polynomials FDEs variable order

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Model order reduction of linear time-varying systems via shifted legendre polynomials

Model order reduction of linear time-varying systems via shi...

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第43届中国控制会议

作者： Man Tang Zhi-Hua Xiao School of Information and Mathematics Yangtze University

In this paper, we present a model order reduction algorithm for linear time-varying systems via shifted legendre polynomials. The main idea of the approach is to use approximate low-rank factors of the finite-time empirical Gramians, which are constructed from the the expansion coefficients of impulse responses in the space spanned by shifted legendre polynomials,to generate approximate balanced system for the large-scale system. Then, the reduced-order model is constructed by truncating the states corresponding to the small approximate Hankel singular values(HSVs). Finally, a numerical experiment is given to demonstrate the effectiveness of the proposed methods.

关键词： Model order reduction time-varying systems Balanced truncation shifted legendre polynomials

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