A Petrov--Galerkin Spectral Method of Linear Complexity for Fractional Multiterm ODEs on the Half Line

DOI10.1137/17M1113060zbMath1367.65108OpenAlexW2618423736MaRDI QIDQ5268984

Mohsen Zayernouri, Anna Lischke, George Em. Karniadakis

Publication date: 14 June 2017

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/17m1113060

zbMATH Keywords

numerical examplessingular solutionslinear complexitydistributed orderGauss-Legendre quadrature rulemultiterm fractional differential equationsLaguerre Petrov-Galerkin spectral methodlinear multiterm fractional initial value problemstunable accuracy

Mathematics Subject Classification ID

Linear ordinary differential equations and systems (34A30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Fractional ordinary differential equations (34A08)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fractional Sturm-Liouville eigen-problems: theory and numerical approximation
• Exponentially accurate spectral and spectral element methods for fractional ODEs
• High-order algorithms for Riesz derivative and their applications. II
• Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative
• Convergence and superconvergence of a fully-discrete scheme for multi-term time fractional diffusion equations
• Fractional Sturm-Liouville boundary value problems in unbounded domains: theory and applications
• A fast algorithm for the inversion of general Toeplitz matrices
• Numerical analysis for distributed-order differential equations
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• A unified Petrov-Galerkin spectral method for fractional PDEs
• The numerical solution of linear multi-term fractional differential equations: Systems of equations
• Analytical solutions of multi-term time fractional differential equations and application to unsteady flows of generalized viscoelastic fluid
• A modified generalized Laguerre spectral method for fractional differential equations on the half line
• A high-order spectral method for the multi-term time-fractional diffusion equations
• Numerical methods for solving the multi-term time-fractional wave-diffusion equation
• Efficient generalized Laguerre-spectral methods for solving multi-term fractional differential equations on the half line
• Discontinuous Spectral Element Methods for Time- and Space-Fractional Advection Equations
• Optimal Error Estimates of Spectral Petrov--Galerkin and Collocation Methods for Initial Value Problems of Fractional Differential Equations
• Spectral Methods
• Spectral Methods for Time-Dependent Problems
• Variational solution of fractional advection dispersion equations on bounded domains in ℝd
• A Space-Time Spectral Method for the Time Fractional Diffusion Equation
• Computational Methods for Integral Equations
• Collocation Methods for Volterra Integral and Related Functional Differential Equations
• Fourth Order Accurate Scheme for the Space Fractional Diffusion Equations
• Tempered Fractional Sturm--Liouville EigenProblems
• Petrov--Galerkin and Spectral Collocation Methods for Distributed Order Differential Equations
• Finite Element Method for the Space and Time Fractional Fokker–Planck Equation
• On a fractional distributed-order oscillator
• Fractional Spectral Collocation Method