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Numerical analysis of a semilinear fractional diffusion equation [article]

Binjie Li, Tao Wang, Xiaoping Xie
2019 arXiv   pre-print
This paper considers the numerical analysis of a semilinear fractional diffusion equation with nonsmooth initial data. A new Grönwall's inequality and its discrete version are proposed.  ...  By the two inequalities, error estimates in three Sobolev norms are derived for a spatial semi-discretization and a full discretization, which are optimal with respect to the regularity of the solution  ...  So far, the numerical analysis for time fractional diffusion-wave equations mainly focuses on the linear problems, and is very rare for semilinear fractional diffusion equations.  ... 
arXiv:1909.00016v1 fatcat:tsplxosszre4ndiowiwvpht5qy

A symmetric fractional-order reduction method for direct nonuniform approximations of semilinear diffusion-wave equations [article]

Pin Lyu, Seakweng Vong
2021 arXiv   pre-print
We introduce a symmetric fractional-order reduction (SFOR) method to construct numerical algorithms on general nonuniform temporal meshes for semilinear fractional diffusion-wave equations.  ...  An adaptive time stepping strategy which based on the (fast linearized) L1 and Alikhanov algorithms is designed for the semilinear diffusion-wave equations.  ...  The equations (3.10)-(3.12) represent two different numerical algorithms for solving the semilinear diffusion-wave equation.  ... 
arXiv:2101.09678v3 fatcat:eyidssjtejcs3a3hew2sbarthy

Contents of Volume 273

2002 Journal of Mathematical Analysis and Applications  
Feldman Energy bounds for some nonstandard problems in partial differential equations 75 Existence and numerical approximations of periodic solutions of semilinear fourth-order differential equations 121  ...  Fridman Spectral analysis and multidimensional stability of traveling waves for nonlocal Allen-Cahn equation 45 Perturbations of hypercyclic vectors 67 N.S.  ...  ChenOn the system of two difference equations x n+1 = k i=0 A i  ... 
doi:10.1016/s0022-247x(02)00487-0 fatcat:zbcwmuogdbaftcgrgfvhttzaly

Page 287 of Mathematical Reviews Vol. , Issue 97A [page]

1997 Mathematical Reviews  
a fast-diffusion equation and stability.  ...  Summary: “The general class of porous medium equations 0S/dt + V-f(S)u-—V-k(S)VS = Q(S), with diffusion coefficient k van- ishing for two values of saturation S and the fractional flow f having a characteristic  ... 

A Priori Estimates for Fractional Nonlinear Degenerate Diffusion Equations on Bounded Domains

Matteo Bonforte, Juan Luis Vázquez
2015 Archive for Rational Mechanics and Analysis  
We investigate quantitative properties of nonnegative solutions u(t, x) ≥ 0 to the nonlinear fractional diffusion equation, ∂ t u + L(u m ) = 0, posed in a bounded domain, x ∈ Ω ⊂ R N for t > 0 and m >  ...  As a byproduct, we derive similar estimates for the elliptic semilinear equation LS m = S and we prove existence and uniqueness of H −s (Ω) solutions via parabolic techniques.  ...  Numerical solution to anisotropic diffusion equations in special cases Lukasz Skonieczny, Uniwersytet Warszawski  ... 
doi:10.1007/s00205-015-0861-2 fatcat:cfwell5n7bbaheb5ftt2cg5xyu

Page 2205 of Mathematical Reviews Vol. , Issue 93d [page]

1993 Mathematical Reviews  
We find no numerical high-frequency modulational instabilities, in addition to the mod- ulational instability from a linear analysis around a nonlinear state for the DNLS equation if the modulation is  ...  Risebro, Nils Henrik (N-OSLO) A method of fractional steps for scalar conservation laws without the CFL condition.  ... 

Complex Boundary Value Problems of Nonlinear Differential Equations: Theory, Computational Methods, and Applications

Xinguang Zhang, Yong Hong Wu, Dragoş-Pătru Covei, Xinan Hao
2013 Abstract and Applied Analysis  
Acknowledgment Here, we would like to thank all the authors and reviewers of the papers for their excellent contributions. Xinguang Zhang Yong Hong Wu Dragos ¸-Pȃtru Covei Xinan Hao  ...  The analysis and numerical results show that the proposed scheme of high order is effective and efficient for the solution of jump-diffusion stochastic delay differential equations.  ...  for a general class of semilinear fractional evolution equations of mixed type with nonlocal conditions on infinite dimensional Banach spaces, by utilizing a new estimation technique of the measure of  ... 
doi:10.1155/2013/705482 fatcat:hkwxefx2rfb73nfflmypdcp3ya

Complex Boundary Value Problems of Nonlinear Differential Equations 2014

Xinguang Zhang, Yong Hong Wu, Dragoș-Pãtru Covei, Xinan Hao
2014 Abstract and Applied Analysis  
In the paper titled "Dynamic analysis and chaos of the 4D fractional-order power system, " the authors study the dynamic analysis of a fractional-order power system with parameter Q1 and firstly report  ...  about bifurcation analysis of the fractional order power system.  ...  In the paper titled "Dynamic analysis and chaos of the 4D fractional-order power system, " the authors study the dynamic analysis of a fractional-order power system with parameter Q1 and firstly report  ... 
doi:10.1155/2014/496350 fatcat:vohr34wmsndohhpsun74csnarm

Page 2070 of Mathematical Reviews Vol. , Issue 2002C [page]

2002 Mathematical Reviews  
Lett. 14 (2001), no. 6, 707-714 Summary: “We describe a numerical method to verify the ex- istence and local uniqueness of solutions of semilinear parabolic equations.  ...  (J-SAGAS-I; Saga Numerical existence and uniqueness proof for solutions of semilinear parabolic equations. (English summary) Appl. Math.  ... 

Recent Advance in Function Spaces and Their Applications in Fractional Differential Equations

Xinguang Zhang, Lishan Liu, Yonghong Wu, Liguang Wang
2019 Journal of Function Spaces  
In the paper titled "Existence Results for a Class of Semilinear Fractional Partial Differential Equations with Delay in Banach Spaces", the authors consider the existence and uniqueness of the mild solutions  ...  for a class of nonlinear time fractional partial differential equations with delay by using the theory of solution operator and the general Banach contraction mapping principle.  ...  Acknowledgments We would like to highly appraise the excellent works of all authors and reviewers. Xinguang Zhang Lishan Liu Yonghong Wu Liguang Wang  ... 
doi:10.1155/2019/5719808 fatcat:mwdi7rybjvabjot56zpesc6f7a

Page 5454 of Mathematical Reviews Vol. , Issue 2003g [page]

2003 Mathematical Reviews  
semilinear parabolic equations.  ...  Summary: “Modern numerical approximations of conservation laws rely on numerical dissipation as a means of stabilization.  ... 

Page 3716 of Mathematical Reviews Vol. , Issue 96f [page]

1996 Mathematical Reviews  
He shows that the method is applicable to semilinear systems. In addition, the method is used on a linear convection-diffusion equation in which convection is one step and diffusion another.  ...  Michael Fréhner (Cottbus) 65 NUMERICAL ANALYSIS 3716 96f:65122 65M12 Storti, Mario; Nigro, Norberto; Idelsohn, Sergio A Petrov-Galerkin formulation for the reaction-advection-diffusion equation.  ... 


Catherine Choquet, Natália Martins, M. Rchid Sidi Ammi, Mouhcine Tilioua, Delfim Torres
2017 Discrete and Continuous Dynamical Systems. Series S  
applications, contributing especially to the theoretical, asymptotic and numerical analysis of partial and fractional differential equations.  ...  Torres • Finite difference and Legendre spectral method for a time-fractional diffusion convection equation for image restoration, by M. R. Sidi Ammi and I.  ... 
doi:10.3934/dcdss.201801i fatcat:ob7maxccsbfw7em3ie27sldd5m

Numerical Methods for Semilinear Fractional Diffusion Equations with Time Delay

global sci
2022 Advances in Applied Mathematics and Mechanics  
In this paper, we consider the numerical solutions of the semilinear Riesz space-fractional diffusion equations (RSFDEs) with time delay, which constitute an important class of differential equations of  ...  Numerical results are presented to verify the accuracy and efficiency of the proposed numerical scheme.  ...  Acknowledgements The work of S. Yang  ... 
doi:10.4208/aamm.oa-2020-0387 fatcat:w7v5yfdyyzd2rhaumyoifkytcq

An ADI compact difference scheme for the two-dimensional semilinear time-fractional mobile–immobile equation

Huifa Jiang, Da Xu, Wenlin Qiu, Jun Zhou
2020 Computational and Applied Mathemathics  
In this paper, an alternating direction implicit (ADI) compact difference scheme will be proposed for solving semilinear time-fractional mobile-immobile equations in two dimensions.  ...  In addition, the accuracy and effectiveness of the scheme are illustrated by several numerical experiments.  ...  implicit numerical methods for a class of fractional advection-dispersion models.  ... 
doi:10.1007/s40314-020-01345-x fatcat:gg2m3hl42jhwncuthp5dtdath4
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