Crank-Nicolson ADI Galerkin Finite Element Methods for Two Classes of Riesz Space Fractional Partial Differential Equations
نویسندگان
چکیده
منابع مشابه
A Crank-Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation
In this paper, a new alternating direction implicit Galerkin–Legendre spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed. The temporal component is discretized by the Crank–Nicolson method. The detailed implementation of the method is presented. The stability and convergence analysis is strictly proven, which shows that the derived ...
متن کاملAn ADI Crank-Nicolson Orthogonal Spline Collocation Method for the Two-Dimensional Fractional Diffusion-Wave Equation
A new method is formulated and analyzed for the approximate solution of a twodimensional time-fractional diffusion-wave equation. In this method, orthogonal spline collocation is used for the spatial discretization and, for the time-stepping, a novel alternating direction implicit (ADI) method based on the Crank-Nicolson method combined with the L1-approximation of the time Caputo derivative of...
متن کاملThe new implicit finite difference scheme for two-sided space-time fractional partial differential equation
Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. S...
متن کاملGalerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
We describe and analyze two numerical methods for a linear elliptic problem with stochastic coefficients and homogeneous Dirichlet boundary conditions. Here the aim of the computations is to approximate statistical moments of the solution, and, in particular, we give a priori error estimates for the computation of the expected value of the solution. The first method generates independent identi...
متن کاملKernel-based Collocation Methods versus Galerkin Finite Element Methods for Approximating Elliptic Stochastic Partial Differential Equations
We compare a kernel-based collocation method (meshfree approximation method) with a Galerkin finite element method for solving elliptic stochastic partial differential equations driven by Gaussian noise. The kernel-based collocation solution is a linear combination of reproducing kernels obtained from related differential and boundary operators centered at chosen collocation points. Its random ...
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: Computer Modeling in Engineering & Sciences
سال: 2020
ISSN: 1526-1506
DOI: 10.32604/cmes.2020.09224