The Tracking of Derivative Discontinuities for Delay Fractional Equations Based on Fitted L1 Method
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Dakang Cen
Abstract
In this paper, the analytic solution of the delay fractional model is derived by the method of steps. The theoretical result implies that the regularity of the solution at s+ is better than that at 0+ , where s is a constant time delay. The behavior of derivative discontinuity is also discussed. Then, improved regularity solution is obtained by the decomposition technique and a fitted L1 numerical scheme is designed for it. For the case of initial singularity, the optimal convergence order is reached on uniform meshes when α∈[23,1) , α is the order of fractional derivative. Furthermore, an improved fitted L1 method is proposed and the region of optimal convergence order is larger. For the case t>s , stability and min{2α,1} order convergence of the fitted L1 scheme are deduced. At last, the numerical tests are carried out and confirm the theoretical result.
Funding statement: This research was funded by the University of Macau (File No. MYRG2020-00035-FST, MYRG2022-00076-FST).
References
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Articles in the same Issue
- Frontmatter
- A Symmetric Interior Penalty Method for an Elliptic Distributed Optimal Control Problem with Pointwise State Constraints
- The Tracking of Derivative Discontinuities for Delay Fractional Equations Based on Fitted L1 Method
- Two-Level Error Estimation for the Integral Fractional Laplacian
- Fractional Laplacian – Quadrature Rules for Singular Double Integrals in 3D
- A Priori Analysis of a Symmetric Interior Penalty Discontinuous Galerkin Finite Element Method for a Dynamic Linear Viscoelasticity Model
- Positivity-Preserving Numerical Method for a Stochastic Multi-Group SIR Epidemic Model
- Implicit-Explicit Finite Difference Approximations of a Semilinear Heat Equation with Logarithmic Nonlinearity
- A Novel Study Based on Shifted Jacobi Polynomials to Find the Numerical Solutions of Nonlinear Stochastic Differential Equations Driven by Fractional Brownian Motion
- On Split Monotone Variational Inclusion Problem with Multiple Output Sets with Fixed Point Constraints
- Local Discontinuous Galerkin Method for a Third-Order Singularly Perturbed Problem of Convection-Diffusion Type
- Simultaneous Inversion of the Space-Dependent Source Term and the Initial Value in a Time-Fractional Diffusion Equation
- A Posteriori Error Estimator for Weak Galerkin Finite Element Method for Stokes Problem Using Diagonalization Techniques
Articles in the same Issue
- Frontmatter
- A Symmetric Interior Penalty Method for an Elliptic Distributed Optimal Control Problem with Pointwise State Constraints
- The Tracking of Derivative Discontinuities for Delay Fractional Equations Based on Fitted L1 Method
- Two-Level Error Estimation for the Integral Fractional Laplacian
- Fractional Laplacian – Quadrature Rules for Singular Double Integrals in 3D
- A Priori Analysis of a Symmetric Interior Penalty Discontinuous Galerkin Finite Element Method for a Dynamic Linear Viscoelasticity Model
- Positivity-Preserving Numerical Method for a Stochastic Multi-Group SIR Epidemic Model
- Implicit-Explicit Finite Difference Approximations of a Semilinear Heat Equation with Logarithmic Nonlinearity
- A Novel Study Based on Shifted Jacobi Polynomials to Find the Numerical Solutions of Nonlinear Stochastic Differential Equations Driven by Fractional Brownian Motion
- On Split Monotone Variational Inclusion Problem with Multiple Output Sets with Fixed Point Constraints
- Local Discontinuous Galerkin Method for a Third-Order Singularly Perturbed Problem of Convection-Diffusion Type
- Simultaneous Inversion of the Space-Dependent Source Term and the Initial Value in a Time-Fractional Diffusion Equation
- A Posteriori Error Estimator for Weak Galerkin Finite Element Method for Stokes Problem Using Diagonalization Techniques
