Galerkin method for time fractional semilinear equations
نویسندگان
چکیده
This paper gathers the tools for solving Riemann-Liouville time fractional non-linear PDE’s by using a Galerkin method. method has advantage of not being more complicated than one used to solve same PDE with first order derivative. As model problem, existence and uniqueness is proved semilinear heat equations polynomial growth at infinity.
منابع مشابه
Wavelet Galerkin Method for Solving Stochastic Fractional Differential Equations
Stochastic fractional differential equations (SFDEs) have many physical applications in the fields of turbulance, heterogeneous, flows and matrials, viscoelasticity and electromagnetic theory. In this paper, a new wavelet Galerkin method is proposed for numerical solution of SFDEs. First, fractional and stochastic operational matrices for the Chebyshev wavelets are introduced. Then, these opera...
متن کاملDiscontinuous Galerkin Method for Fractional Convection-Diffusion Equations
We propose a discontinuous Galerkin method for fractional convection-diffusion equations with a superdiffusion operator of order α(1 < α < 2) defined through the fractional Laplacian. The fractional operator of order α is expressed as a composite of first order derivatives and a fractional integral of order 2 − α. The fractional convection-diffusion problem is expressed as a system of low order...
متن کاملThe discontinuous Galerkin method for fractional degenerate convection-diffusion equations
We propose and study discontinuous Galerkin methods for strongly degenerate convection-diffusion equations perturbed by a fractional diffusion (Lévy) operator. We prove various stability estimates along with convergence results toward properly defined (entropy) solutions of linear and nonlinear equations. Finally, the qualitative behavior of solutions of such equations are illustrated through n...
متن کاملSolving nonlinear space-time fractional differential equations via ansatz method
In this paper, the fractional partial differential equations are defined by modified Riemann-Liouville fractional derivative. With the help of fractional derivative and fractional complex transform, these equations can be converted into the nonlinear ordinary differential equations. By using solitay wave ansatz method, we find exact analytical solutions of the space-time fractional Zakharov Kuz...
متن کاملDiscontinuous Galerkin Methods for Fractional Diffusion Equations
We consider the development and analysis of local discontinuous Galerkin methods for fractional diffusion problems, characterized by having fractional derivatives, parameterized by β ∈ [1, 2]. We show through analysis that one can construct a numerical flux which results in a scheme that exhibit optimal order of convergence O(hk+1) in the continuous range between pure advection (β = 1) and pure...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fractional Calculus and Applied Analysis
سال: 2021
ISSN: ['1311-0454', '1314-2224']
DOI: https://doi.org/10.1515/fca-2021-0033