A static memory sparse spectral method for time-fractional PDEs
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Publication:6087942
DOI10.1016/j.jcp.2023.112522arXiv2304.06855OpenAlexW4387339091MaRDI QIDQ6087942
Timon S. Gutleb, José Antonio Carrillo
Publication date: 16 November 2023
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2304.06855
orthogonal polynomialsspectral methodfractional derivativeCaputo derivativesparsefractional PDEtime-fractionalbandedhistory-free
Numerical approximation and computational geometry (primarily algorithms) (65Dxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Approximations and expansions (41Axx)
Cites Work
- Unnamed Item
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- Hitchhiker's guide to the fractional Sobolev spaces
- Ten equivalent definitions of the fractional Laplace operator
- A fast and well-conditioned spectral method for singular integral equations
- The automatic solution of partial differential equations using a global spectral method
- Quadrature formulae on half-infinite intervals
- An investigation of some nonclassical methods for the numerical approximation of Caputo-type fractional derivatives
- On a critique of a numerical scheme for the calculation of fractionally damped dynamical systems
- The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
- Treatment of dynamic systems with fractional derivatives without evaluating memory-integrals
- Computation of fractional derivatives using Fourier transform and digital FIR differentiator.
- Tensor calculus in polar coordinates using Jacobi polynomials
- Generalizations of orthogonal polynomials
- An improved non-classical method for the solution of fractional differential equations
- A new and sharper bound for Legendre expansion of differentiable functions
- How much faster does the best polynomial approximation converge than Legendre projection?
- A fast sparse spectral method for nonlinear integro-differential Volterra equations with general kernels
- Recurrence relations for a family of orthogonal polynomials on a triangle
- A new family of orthogonal polynomials in three variables
- A contour method for time-fractional PDEs and an application to fractional viscoelastic beam equations
- Fractional derivative models for atmospheric dispersion of pollutants
- Orthogonal structure on a wedge and on the boundary of a square
- Wave field simulation for heterogeneous porous media with singular memory drag force
- Wave field simulation for heterogeneous transversely isotropic porous media with the JKD dynamic permeability
- The numerical solution of fractional integral equations via orthogonal polynomials in fractional powers
- Fast computation of Gauss quadrature nodes and weights on the whole real line
- On the Optimal Estimates and Comparison of Gegenbauer Expansion Coefficients
- Sharp Error Bounds for Jacobi Expansions and Gegenbauer--Gauss Quadrature of Analytic Functions
- A Fast and Well-Conditioned Spectral Method
- Iteration-Free Computation of Gauss--Legendre Quadrature Nodes and Weights
- On Error Bounds for Orthogonal Polynomial Expansions and Gauss-Type Quadrature
- Julia: A Fresh Approach to Numerical Computing
- A Sparse Spectral Method for Volterra Integral Equations Using Orthogonal Polynomials on the Triangle
- A Fast Algorithm for the Calculation of the Roots of Special Functions
- A Fast and Spectrally Convergent Algorithm for Rational-Order Fractional Integral and Differential Equations
- Beugungstheorie des schneidenver-fahrens und seiner verbesserten form, der phasenkontrastmethode
- Orthogonal structure on a quadratic curve
- Sparse spectral methods for partial differential equations on spherical caps
- Computing equilibrium measures with power law kernels
- Orthogonal polynomials in and on a quadratic surface of revolution
- Sparse spectral and ‐finite element methods for partial differential equations on disk slices and trapeziums
- A Sparse Spectral Method on Triangles
- An ultraspherical spectral method for linear Fredholm and Volterra integro-differential equations of convolution type
- On the convergence rates of Legendre approximation
- Fractional Calculus
- Orthogonal Polynomials of Several Variables
- Note on Backward Recurrence Algorithms
- Fast algorithms using orthogonal polynomials
- The numerical solution of fractional differential equations: speed versus accuracy
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