SPECTRAL_METHOD

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Efficient Finite Difference/Spectral Method for the Time Fractional Ito Equation Using Fast Fourier Transform Technic
《Communications on Applied Mathematics and Computation》2023年第4期1591-1600,共10页Dakang Cen Zhibo Wang Seakweng Vong 
the National Natural Science Foundation of China(No.11701103);the Young Top-notch Talent Program of Guangdong Province of China(No.2017GC010379);the Natural Science Foundation of Guangdong Province of China(No.2022A1515012147);the Project of Science and Technology of Guangzhou of China(No.202102020704);the Opening Project of Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University of China(2021023);the Science and Technology Development Fund,Macao SAR(File No.0005/2019/A);the University of Macao of China(File Nos.MYRG2020-00035-FST,MYRG2018-00047-FST).
A finite difference/spectral scheme is proposed for the time fractional Ito equation.The mass conservation and stability of the numerical solution are deduced by the energy method in the L^(2)norm form.To reduce the c...
关键词：Time fractional Ito equation Finite difference method Spectral method STABILITY 
Conservative Discontinuous Galerkin/Hermite Spectral Method for the Vlasov-Poisson System
《Communications on Applied Mathematics and Computation》2022年第1期34-59,共26页Francis Filbet Tao Xiong 
the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 under Grant Agreement No.633053.;the Science Challenge Project(No.TZ2016002);the National Natural Science Foundation of China(No.11971025);the Natural Science Foundation of Fujian Province(No.2019J06002);the NSAF(No.U1630247)。
We propose a class of conservative discontinuous Galerkin methods for the Vlasov-Pois-son system written as a hyperbolic system using Hermite polynomials in the velocity vari-able.These schemes are designed to be syst...
关键词：Energy conserving Discontinuous Galerkin method Hermite spectral method Vlasov-Poisson 
A Unified Petrov-Galerkin Spectral Method and Fast Solver for Distributed-Order Partial Differential Equations
《Communications on Applied Mathematics and Computation》2021年第1期61-90,共30页Mehdi Samiee Ehsan Kharazmi Mark M.Meerschaert Mohsen Zayernouri 
This work was supported by the AFOSR Young Investigator Program(YIP)award(FA9550-17-1-0150),the MURI/ARO(W911NF-15-1-0562);tthe National Science Foundation Award(DMS-1923201);the ARO Young Investigator Program Award(W911NF-19-1-0444)。
Fractional calculus and fractional-order modeling provide effective tools for modeling and simulation of anomalous diffusion with power-law scalings.In complex multi-fractal anomalous transport phenomena,distributed-o...
关键词：Distributed Sobolev space Well-posedness analysis Discrete inf-sup condition Spectral convergence Jacobi poly-fractonomials Legendre polynomials 
Second-Order Finite Difference/Spectral Element Formulation for Solving the Fractional Advection-Diffusion Equation
《Communications on Applied Mathematics and Computation》2020年第4期653-669,共17页Mostafa Abbaszadeh Hanieh Amjadian 
The authors are grateful to the two reviewers for carefully reading this paper and for their comments and suggestions which have highly improved the paper.
The main aim of this paper is to analyze the numerical method based upon the spectral element technique for the numerical solution of the fractional advection-diffusion equa-tion.The time variable has been discretized...
关键词：Spectral method Finite diference method Fractional advection-difusion equation Galerkin weak form Unconditional stability 
A Semi-Lagrangian Spectral Method for the Vlasov-Poisson System Based on Fourier, Legendre and Hermite Polynomials
《Communications on Applied Mathematics and Computation》2019年第3期333-360,共28页Lorella Fatone Daniele Funaro Gianmarco Manzini 
In this work, we apply a semi-Lagrangian spectral method for the Vlasov-Poisson system, previously designed for periodic Fourier discretizations, by implementing Legendre polynomials and Hermite functions in the appro...
关键词：Spectral METHODS SEMI-LAGRANGIAN METHODS HIGH-ORDER HERMITE functions Vlasov-Poisson equations Mass conservation 
A New Spectral Method Using Nonstandard Singular Basis Functions for Time-Fractional Differential Equations
《Communications on Applied Mathematics and Computation》2019年第2期207-230,共24页Wenjie Liu Li-Lian Wang Shuhuang Xiang 
the China Postdoctoral Science Foundation Funded Project (No.2017M620113);the National Natural Science Foundation of China (Nos.11801120,71773024 and 11771107);the Fundamental Research Funds for the Central Universities (Grant No.HIT.NSRIF.2019058);the Natural Science Foundation of Heilongjiang Province of China (No.G2018006);Singapore MOE AcRF Tier 2 Grants (MOE2017-T2-2-014 and MOE2018-T2-1-059);National Science Foundation of China (No.11371376);the Innovation-Driven Project and Mathematics.
In this paper,we introduce new non-polynomial basis functions for spectral approximation of time-fractional partial differential equations (PDEs). Different from many other approaches,the nonstandard singular basis fu...
关键词：FRACTIONAL differential equations Generalised BIRKHOFF interpolation NONSTANDARD SINGULAR basis function 
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