Error Analysis of a Finite Difference Method on Graded Meshes for a Multiterm Time-Fractional Initial-Boundary Value Problem
-
Chaobao Huang
,
Xiaohui Liu
Abstract
An initial-boundary value problem, whose differential equation contains a sum of fractional time derivatives with orders between 0 and 1, is considered.
Its spatial domain is
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11801332
Award Identifier / Grant number: 11971259
Award Identifier / Grant number: NSAF-U1930402
Funding statement: The research of Martin Stynes is supported in part by the National Natural Science Foundation of China under grant NSAF U1930402. The research of Chaobao Huang is supported in part by the National Natural Science Foundation of China (Grant Nos. 11801332 and 11971259).
Acknowledgements
We thank both reviewers for their careful reading of the paper, and in particular we thank one reviewer for suggesting to us a significant simplification in the stability analysis.
References
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Editorial
- Modern Problems of Numerical Analysis. On the Centenary of the Birth of Alexander Andreevich Samarskii
- Special Issue Articles
- Finite Difference Approximation of a Generalized Time-Fractional Telegraph Equation
- Weighted Estimates for Boundary Value Problems with Fractional Derivatives
- Lagrangian Mixed Finite Element Methods for Nonlinear Thin Shell Problems
- Reliable Computer Simulation Methods for Electrostatic Biomolecular Models Based on the Poisson–Boltzmann Equation
- Adaptive Space-Time Finite Element Methods for Non-autonomous Parabolic Problems with Distributional Sources
- On Convergence of Difference Schemes for Dirichlet IBVP for Two-Dimensional Quasilinear Parabolic Equations with Mixed Derivatives and Generalized Solutions
- Difference Schemes on Uniform Grids for an Initial-Boundary Value Problem for a Singularly Perturbed Parabolic Convection-Diffusion Equation
- A Finite Element Splitting Method for a Convection-Diffusion Problem
- Incomplete Iterative Implicit Schemes
- Explicit Runge–Kutta Methods Combined with Advanced Versions of the Richardson Extrapolation
- Regular Research Articles
- A General Superapproximation Result
- A First-Order Explicit-Implicit Splitting Method for a Convection-Diffusion Problem
- A Factorization of Least-Squares Projection Schemes for Ill-Posed Problems
- A New Mixed Functional-probabilistic Approach for Finite Element Accuracy
- Error Analysis of a Finite Difference Method on Graded Meshes for a Multiterm Time-Fractional Initial-Boundary Value Problem
- A Finite Element Method for Elliptic Dirichlet Boundary Control Problems
Artikel in diesem Heft
- Frontmatter
- Editorial
- Modern Problems of Numerical Analysis. On the Centenary of the Birth of Alexander Andreevich Samarskii
- Special Issue Articles
- Finite Difference Approximation of a Generalized Time-Fractional Telegraph Equation
- Weighted Estimates for Boundary Value Problems with Fractional Derivatives
- Lagrangian Mixed Finite Element Methods for Nonlinear Thin Shell Problems
- Reliable Computer Simulation Methods for Electrostatic Biomolecular Models Based on the Poisson–Boltzmann Equation
- Adaptive Space-Time Finite Element Methods for Non-autonomous Parabolic Problems with Distributional Sources
- On Convergence of Difference Schemes for Dirichlet IBVP for Two-Dimensional Quasilinear Parabolic Equations with Mixed Derivatives and Generalized Solutions
- Difference Schemes on Uniform Grids for an Initial-Boundary Value Problem for a Singularly Perturbed Parabolic Convection-Diffusion Equation
- A Finite Element Splitting Method for a Convection-Diffusion Problem
- Incomplete Iterative Implicit Schemes
- Explicit Runge–Kutta Methods Combined with Advanced Versions of the Richardson Extrapolation
- Regular Research Articles
- A General Superapproximation Result
- A First-Order Explicit-Implicit Splitting Method for a Convection-Diffusion Problem
- A Factorization of Least-Squares Projection Schemes for Ill-Posed Problems
- A New Mixed Functional-probabilistic Approach for Finite Element Accuracy
- Error Analysis of a Finite Difference Method on Graded Meshes for a Multiterm Time-Fractional Initial-Boundary Value Problem
- A Finite Element Method for Elliptic Dirichlet Boundary Control Problems
