A collocation method based on cubic trigonometric B-splines for the numerical simulation of the time-fractional diffusion equation
DOI10.1186/s13662-021-03360-6zbMath1494.65073OpenAlexW3165264694MaRDI QIDQ2166931
Muhammad Yaseen, Muhammad Abbas, Muhammad Bilal Riaz
Publication date: 25 August 2022
Published in: Advances in Difference Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1186/s13662-021-03360-6
stabilityconvergencespline approximationstime-fractional diffusion equationcubic trigonometric B-spline method
Fractional derivatives and integrals (26A33) 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) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Fractional partial differential equations (35R11)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The application of cubic trigonometric B-spline to the numerical solution of the hyperbolic problems
- A numerical solution to fractional diffusion equation for force-free case
- A compact finite difference scheme for the fractional sub-diffusion equations
- Implicit difference approximation for the time fractional diffusion equation
- Implicit finite difference approximation for time fractional diffusion equations
- A practical guide to splines
- Fractals and fractional calculus in continuum mechanics
- Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
- A finite difference scheme based on cubic trigonometric B-splines for a time fractional diffusion-wave equation
- A numerical method based on fully discrete direct discontinuous Galerkin method for the time fractional diffusion equation
- A fully implicit finite difference scheme based on extended cubic B-splines for time fractional advection-diffusion equation
- A cubic trigonometric B-spline collocation approach for the fractional sub-diffusion equations
- The accuracy and stability of an implicit solution method for the fractional diffusion equation
- Non-polynomial quintic spline for solving fourth-order fractional boundary value problems involving product terms
- A fourth order non-polynomial quintic spline collocation technique for solving time fractional superdiffusion equations
- Extended cubic B-splines in the numerical solution of time fractional telegraph equation
- A numerical algorithm based on modified extended B-spline functions for solving time-fractional diffusion wave equation involving reaction and damping terms
- A new difference scheme for time fractional heat equations based on the Crank-Nicholson method
- Non-polynomial quintic spline for numerical solution of fourth-order time fractional partial differential equations
- A Fourier method for the fractional diffusion equation describing sub-diffusion
- Weighted average finite difference methods for fractional diffusion equations
- A speculative study of 2∕3-order fractional Laplacian modeling of turbulence: Some thoughts and conjectures
- An Explicit Finite Difference Method and a New von Neumann-Type Stability Analysis for Fractional Diffusion Equations
- The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
- An efficient computational technique based on cubic trigonometric B-splines for time fractional Burgers' equation
- A Discontinuous Petrov--Galerkin Method for Time-Fractional Diffusion Equations
- A pseudo-spectral scheme for the approximate solution of a time-fractional diffusion equation
- Numerical solution of time-fractional fourth-order partial differential equations
- The random walk's guide to anomalous diffusion: A fractional dynamics approach
