Numerical methods for fractional partial differential equations
In this review paper, we are mainly concerned with the finite difference methods, the
Galerkin finite element methods, and the spectral methods for fractional partial differential …
Galerkin finite element methods, and the spectral methods for fractional partial differential …
An approach to construct higher order time discretisation schemes for time fractional partial differential equations with nonsmooth data
In this paper, we shall review an approach by which we can seek higher order time
discretisation schemes for solving time fractional partial differential equations with …
discretisation schemes for solving time fractional partial differential equations with …
Second-order numerical methods for multi-term fractional differential equations: smooth and non-smooth solutions
Starting with the asymptotic expansion of the error equation of the shifted Grünwald–
Letnikov formula, we derive a new modified weighted shifted Grünwald–Letnikov (WSGL) …
Letnikov formula, we derive a new modified weighted shifted Grünwald–Letnikov (WSGL) …
A stable fast time-stepping method for fractional integral and derivative operators
A unified fast time-stepping method for both fractional integral and derivative operators is
proposed. The fractional operator is decomposed into a local part with memory …
proposed. The fractional operator is decomposed into a local part with memory …
A simple solver for the fractional Laplacian in multiple dimensions
We present a simple discretization scheme for the hypersingular integral representa-tion of
the fractional Laplace operator and solver for the corresponding fractional Laplacian …
the fractional Laplace operator and solver for the corresponding fractional Laplacian …
Numerical approach to chaotic pattern formation in diffusive predator–prey system with Caputo fractional operator
KM Owolabi - Numerical Methods for Partial Differential …, 2021 - Wiley Online Library
This paper is primarily concern with the formulation and analysis of a reliable numerical
method based on the novel alternating direction implicit finite difference scheme for the …
method based on the novel alternating direction implicit finite difference scheme for the …
Time two-mesh algorithm combined with finite element method for time fractional water wave model
In this article, a new time two-mesh (TT-M) finite element (FE) method, which is constructed
by a new TT-M algorithm and FE method in space, is proposed and analyzed. The numerical …
by a new TT-M algorithm and FE method in space, is proposed and analyzed. The numerical …
An H2N2 interpolation for Caputo derivative with order in (1, 2) and its application to time-fractional wave equations in more than one space dimension
In this paper, a new derived method is developed for a known numerical differential formula
of the Caputo fractional derivative of order γ ∈ (1, 2) γ∈(1, 2)(Li and Zeng in Numerical …
of the Caputo fractional derivative of order γ ∈ (1, 2) γ∈(1, 2)(Li and Zeng in Numerical …
Chaotic and spatiotemporal oscillations in fractional reaction-diffusion system
KM Owolabi, B Karaagac - Chaos, Solitons & Fractals, 2020 - Elsevier
This paper focuses on the design and analysis of an efficient numerical method based on
the novel implicit finite difference scheme for the solution of the dynamics of reaction …
the novel implicit finite difference scheme for the solution of the dynamics of reaction …
High-order local discontinuous Galerkin method combined with WSGD-approximation for a fractional subdiffusion equation
In this paper, a high-order local discontinuous Galerkin (LDG) method combined with
weighted and shifted Grünwald difference (WSGD) approximation is developed and …
weighted and shifted Grünwald difference (WSGD) approximation is developed and …