A novel numerical technique for solving time fractional nonlinear diffusion equations involving weak singularities
DOI10.1002/MMA.9214OpenAlexW4327965766MaRDI QIDQ6178225
Publication date: 18 January 2024
Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/mma.9214
error estimatesFisher's equationCaputo derivativeAllen-Cahn modelweak singularity\(\mathrm{L}1\) schemeDGJ methodfractional nonlinear diffusion
PDEs in connection with fluid mechanics (35Q35) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Fractional derivatives and integrals (26A33) Partial functional-differential equations (35R10) 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) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Finite difference methods for boundary value problems involving PDEs (65N06) Singularity in context of PDEs (35A21) Fractional partial differential equations (35R11)
Cites Work
- Unnamed Item
- Unnamed Item
- An analytic algorithm for time fractional nonlinear reaction-diffusion equation based on a new iterative method
- A numerical approach for solving the fractional Fisher equation using Chebyshev spectral collocation method
- An iterative method for solving nonlinear functional equations
- Phase-field simulations of interfacial dynamics in viscoelastic fluids using finite elements with adaptive meshing
- The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
- New approach for exact solutions of time fractional Cahn-Allen equation and time fractional phi-4 equation
- NURBS curves with the application of multiple bones fracture reconstruction
- A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method
- A numerical investigation of Caputo time fractional Allen-Cahn equation using redefined cubic B-spline functions
- Adomian decomposition and homotopy perturbation method for the solution of time fractional partial integro-differential equations
- A sharp \(\alpha\)-robust \(L^\infty (H^1)\) error bound for a time-fractional Allen-Cahn problem discretised by the Alikhanov \(L2-1_\sigma\) scheme and a standard FEM
- Time-fractional Allen-Cahn and Cahn-Hilliard phase-field models and their numerical investigation
- Optimal \(H^1\) spatial convergence of a fully discrete finite element method for the time-fractional Allen-Cahn equation
- Time-fractional Allen-Cahn equations: analysis and numerical methods
- Numerical analysis of linear and nonlinear time-fractional subdiffusion equations
- Fast explicit operator splitting method and time-step adaptivity for fractional non-local Allen-Cahn model
- Linearized Galerkin FEMs for nonlinear time fractional parabolic problems with non-smooth solutions in time direction
- Finite difference/spectral approximations for the time-fractional diffusion equation
- The fractional natural decomposition method: theories and applications
- Numerical Analysis of Nonlinear Subdiffusion Equations
- Analysis of the L1 scheme for a time fractional parabolic–elliptic problem involving weak singularity
- On Energy Dissipation Theory and Numerical Stability for Time-Fractional Phase-Field Equations
- Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
This page was built for publication: A novel numerical technique for solving time fractional nonlinear diffusion equations involving weak singularities
