Fourth-order time stepping methods with matrix transfer technique for space-fractional reaction-diffusion equations
DOI10.1016/j.apnum.2019.07.006zbMath1431.65194OpenAlexW2961309919WikidataQ127519573 ScholiaQ127519573MaRDI QIDQ2273073
S. S. Alzahrani, Toheeb Biala, Khaled M. Furati, Abdul Q. M. Khaliq
Publication date: 18 September 2019
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.apnum.2019.07.006
Runge-Kutta methodfractional Laplacianmatrix transfer techniquetime stepping methodsnon-smooth initial dataspace-fractional reaction-diffusion equations
Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Padé approximation (41A21) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Fractional partial differential equations (35R11)
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- Uniqueness of non-linear ground states for fractional Laplacians in \(\mathbb{R}\)
- New numerical methods for the Riesz space fractional partial differential equations
- Fourier spectral methods for fractional-in-space reaction-diffusion equations
- Higher order exponential time differencing scheme for system of coupled nonlinear Schrödinger equations
- Exponential time differencing for stiff systems
- Positive solutions of nonlinear problems involving the square root of the Laplacian
- A parallel block cyclic reduction algorithm for the fast solution of elliptic equations
- A new class of time discretization schemes for the solution of nonlinear PDEs
- Blow-up and global solutions for a class of time fractional nonlinear reaction-diffusion equation with weakly spatial source
- Adaptive moving mesh computations for reaction--diffusion systems
- Finite difference approximations for fractional advection-dispersion flow equations
- A linearly implicit predicator-corrector method for reaction-diffusion equations
- Linearly implicit predictor-corrector methods for space-fractional reaction-diffusion equations with non-smooth initial data
- A novel compact numerical method for solving the two-dimensional non-linear fractional reaction-subdiffusion equation
- A PDE approach to fractional diffusion in general domains: a priori error analysis
- A second-order accurate numerical approximation for the fractional diffusion equation
- Novel Numerical Methods for Solving the Time-Space Fractional Diffusion Equation in Two Dimensions
- An Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations
- Pattern formation in the one-dimensional Gray - Scott model
- On parallel algorithms for semidiscretized parabolic partial differential equations based on subdiagonal Padé approximations
- The Extrapolation of First Order Methods for Parabolic Partial Differential Equations. I
- Numerical methods for fractional partial differential equations
- Fourth-order methods for space fractional reaction–diffusion equations with non-smooth data
- High Accuracy Spectral Method for the Space-Fractional Diffusion Equations
- Finite Element Method for the Space and Time Fractional Fokker–Planck Equation
- Numerical Approximation of a Time Dependent, Nonlinear, Space‐Fractional Diffusion Equation
- Nonlinear equations for fractional Laplacians II: Existence, uniqueness, and qualitative properties of solutions
- A real distinct poles exponential time differencing scheme for reaction-diffusion systems