Super-Exponentially Convergent Parallel Algorithm for a Fractional Eigenvalue Problem of Jacobi-Type
-
Ivan Gavrilyuk
,
Volodymyr Makarov
and
Nataliia Romaniuk
Abstract
A new algorithm for eigenvalue problems for the fractional Jacobi-type ODE is proposed.
The algorithm is based on piecewise approximation of the coefficients of the differential equation with subsequent recursive procedure adapted from some homotopy considerations.
As a result, the eigenvalue problem (which is in fact nonlinear) is replaced by a sequence of linear boundary value problems (besides the first one) with a singular linear operator called the exact functional discrete scheme (EFDS).
A finite subsequence of m terms, called truncated functional discrete scheme (TFDS), is the basis for our algorithm.
The approach provides super-exponential convergence rate as
Acknowledgements
We want to thank the anonymous referees for their helpful remarks which contributed to improvement of the article.
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Space-Time Petrov–Galerkin FEM for Fractional Diffusion Problems
- Super-Exponentially Convergent Parallel Algorithm for a Fractional Eigenvalue Problem of Jacobi-Type
- Convergence in Positive Time for a Finite Difference Method Applied to a Fractional Convection-Diffusion Problem
- Müntz Spectral Methods for the Time-Fractional Diffusion Equation
- Finite Difference Methods for the Generator of 1D Asymmetric Alpha-Stable Lévy Motions
- The Numerical Computation of the Time Fractional Schrödinger Equation on an Unbounded Domain
- Sparse Optimal Control for Fractional Diffusion
- Numerical Solution of Time-Dependent Problems with Fractional Power Elliptic Operator
- Some Time Stepping Methods for Fractional Diffusion Problems with Nonsmooth Data
- A High-Order Difference Scheme for the Space and Time Fractional Bloch–Torrey Equation
Articles in the same Issue
- Frontmatter
- Space-Time Petrov–Galerkin FEM for Fractional Diffusion Problems
- Super-Exponentially Convergent Parallel Algorithm for a Fractional Eigenvalue Problem of Jacobi-Type
- Convergence in Positive Time for a Finite Difference Method Applied to a Fractional Convection-Diffusion Problem
- Müntz Spectral Methods for the Time-Fractional Diffusion Equation
- Finite Difference Methods for the Generator of 1D Asymmetric Alpha-Stable Lévy Motions
- The Numerical Computation of the Time Fractional Schrödinger Equation on an Unbounded Domain
- Sparse Optimal Control for Fractional Diffusion
- Numerical Solution of Time-Dependent Problems with Fractional Power Elliptic Operator
- Some Time Stepping Methods for Fractional Diffusion Problems with Nonsmooth Data
- A High-Order Difference Scheme for the Space and Time Fractional Bloch–Torrey Equation
