An efficient spline collocation method for a nonlinear fourth-order reaction subdiffusion equation
From MaRDI portal
Publication:2204556
DOI10.1007/s10915-020-01308-8zbMath1450.65092OpenAlexW3088863664MaRDI QIDQ2204556
Xuehua Yang, Da Xu, Hai-xiang Zhang
Publication date: 15 October 2020
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10915-020-01308-8
Numerical computation using splines (65D07) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Fractional derivatives and integrals (26A33) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61) Fractional partial differential equations (35R11)
Related Items (10)
A Survey of the L1 Scheme in the Discretisation of Time-Fractional Problems ⋮ Discrete singular convolution for fourth-order multi-term time fractional equation ⋮ A robust error analysis of the OSC method for a multi-term fourth-order sub-diffusion equation ⋮ A formally second‐order <scp>backward differentiation formula</scp> Sinc‐collocation method for the Volterra integro‐differential equation with a weakly singular kernel based on the double exponential transformation ⋮ A high-order two-grid difference method for nonlinear time-fractional biharmonic problems and its unconditional \(\alpha\)-robust error estimates ⋮ A high-order discrete energy decay and maximum-principle preserving scheme for time fractional Allen-Cahn equation ⋮ Numerical solution of highly non-linear fractional order reaction advection diffusion equation using the cubic B-spline collocation method ⋮ Analysis of BDF2 finite difference method for fourth-order integro-differential equation ⋮ Error estimates of a continuous Galerkin time stepping method for subdiffusion problem ⋮ A spectral order method for solving the nonlinear fourth-order time-fractional problem
Cites Work
- Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
- An ADI Crank-Nicolson orthogonal spline collocation method for the two-dimensional fractional diffusion-wave equation
- Existence of nontrivial solutions of an asymptotically linear fourth-order elliptic equation
- Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
- An improved algorithm based on finite difference schemes for fractional boundary value problems with nonsmooth solution
- Local discontinuous Galerkin method for a nonlinear time-fractional fourth-order partial differential equation
- A higher order numerical method for time fractional partial differential equations with nonsmooth data
- The temporal second order difference schemes based on the interpolation approximation for the time multi-term fractional wave equation
- Collocation methods for parabolic equations in a single space variable. Based on C\(^1\)-piecewise-polynomial spaces
- BDF ADI orthogonal spline collocation scheme for the fractional integro-differential equation with two weakly singular kernels
- A relaxation-type Galerkin FEM for nonlinear fractional Schrödinger equations
- Superconvergence points for the spectral interpolation of Riesz fractional derivatives
- Numerical schemes for solving the time-fractional dual-phase-lagging heat conduction model in a double-layered nanoscale thin film
- Nonconforming virtual element method for the time fractional reaction-subdiffusion equation with non-smooth data
- An alternating direction implicit orthogonal spline collocation method for the two dimensional multi-term time fractional integro-differential equation
- Time two-grid algorithm based on finite difference method for two-dimensional nonlinear fractional evolution equations
- Unconditional convergence of a fast two-level linearized algorithm for semilinear subdiffusion equations
- Linearized Galerkin FEMs for nonlinear time fractional parabolic problems with non-smooth solutions in time direction
- An exponentially convergent scheme in time for time fractional diffusion equations with non-smooth initial data
- A high-order method with a temporal nonuniform mesh for a time-fractional Benjamin-Bona-Mahony equation
- Error analysis and numerical simulations of Strang splitting method for space fractional nonlinear Schrödinger equation
- An efficient space-time method for time fractional diffusion equation
- Numerical algorithms with high spatial accuracy for the fourth-order fractional sub-diffusion equations with the first Dirichlet boundary conditions
- A $C^1 $ Finite Element Collocation Method for Elliptic Equations
- Analysis of alternating direction collocation methods for parabolic and hyperbolic problems in two space variables
- An Analysis of the Modified L1 Scheme for Time-Fractional Partial Differential Equations with Nonsmooth Data
- A Discrete Grönwall Inequality with Applications to Numerical Schemes for Subdiffusion Problems
- Sharp Error Estimate of the Nonuniform L1 Formula for Linear Reaction-Subdiffusion Equations
- High‐order ADI orthogonal spline collocation method for a new 2D fractional integro‐differential problem
- Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation
- Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
- Error analysis of the L1 method on graded and uniform meshes for a fractional-derivative problem in two and three dimensions
- Compact Finite Difference Scheme for the Fourth-Order Fractional Subdiffusion System
This page was built for publication: An efficient spline collocation method for a nonlinear fourth-order reaction subdiffusion equation
