A unified Petrov-Galerkin spectral method for fractional PDEs

From MaRDI portal
Publication:1667532

DOI10.1016/j.cma.2014.10.051zbMath1425.65127OpenAlexW2040558735MaRDI QIDQ1667532

George Em. Karniadakis, Mohsen Zayernouri, Mark Ainsworth

Publication date: 30 August 2018

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2014.10.051




Related Items (74)

Spectral element technique for nonlinear fractional evolution equation, stability and convergence analysisA viscoelastic Timoshenko beam: Model development, analysis, and investigationCharacterization of image spaces of Riemann-Liouville fractional integral operators on Sobolev spaces \(W^{m,p} (\Omega)\)Numerical simulation for fractional-order differential system of a glioblastoma multiforme and immune systemNumerical methods for nonlocal and fractional modelsA Priori Error Estimates for Spectral Galerkin Approximations of Integral State-Constrained Fractional Optimal Control ProblemsNumerical solution of distributed order fractional differential equations by hybrid functionsNumerical approximation of higher-order time-fractional telegraph equation by using a combination of a geometric approach and method of lineA Generalized Spectral Collocation Method with Tunable Accuracy for Variable-Order Fractional Differential EquationsStability and convergence of a Crank-Nicolson finite volume method for space fractional diffusion equationsA review of operational matrices and spectral techniques for fractional calculusA fully spectral collocation approximation for multi-dimensional fractional Schrödinger equationsLogarithmic Jacobi collocation method for Caputo-Hadamard fractional differential equationsAn efficient Galerkin spectral method for two-dimensional fractional nonlinear reaction-diffusion-wave equationTwo high-order time discretization schemes for subdiffusion problems with nonsmooth dataA single-step correction scheme of Crank-Nicolson convolution quadrature for the subdiffusion equationDPG method with optimal test functions for a fractional advection diffusion equationA unified Petrov-Galerkin spectral method and fast solver for distributed-order partial differential equationsAn approach to construct higher order time discretisation schemes for time fractional partial differential equations with nonsmooth dataNumerical simulation method of lines together with a pseudospectral method for solving space-time partial differential equations with space left- and right-sided fractional derivativeAnalysis and efficient implementation of alternating direction implicit finite volume method for Riesz space‐fractional diffusion equations in two space dimensionsAn analysis of the L1 scheme for stochastic subdiffusion problem driven by integrated space-time white noiseFractional spectral and pseudo-spectral methods in unbounded domains: theory and applicationsA re-scaling spectral collocation method for the nonlinear fractional pantograph delay differential equations with non-smooth solutionsCorrection of High-Order BDF Convolution Quadrature for Fractional Evolution EquationsSpace-time Petrov-Galerkin FEM for fractional diffusion problemsMüntz spectral methods for the time-fractional diffusion equationAn Analysis of the Modified L1 Scheme for Time-Fractional Partial Differential Equations with Nonsmooth DataA higher order numerical method for time fractional partial differential equations with nonsmooth dataGeneralized Jacobi Spectral Galerkin Method for Fractional-Order Volterra Integro-Differential Equations with Weakly Singular KernelsA fast finite volume method for conservative space-time fractional diffusion equations discretized on space-time locally refined meshesA Petrov-Galerkin finite element-meshfree formulation for multi-dimensional fractional diffusion equationsShifted Jacobi-Gauss-collocation with convergence analysis for fractional integro-differential equationsMüntz pseudo-spectral method: theory and numerical experimentsA unified spectral method for FPDEs with two-sided derivatives. I: A fast solverA unified spectral method for FPDEs with two-sided derivatives. II: Stability, and error analysisNumerical analysis of two Galerkin discretizations with graded temporal grids for fractional evolution equationsHigh-order Time Stepping Schemes for Semilinear Subdiffusion EquationsOptimal stabilization and time step constraints for the forward Euler-local discontinuous Galerkin method applied to fractional diffusion equationsNumerical methods for time-fractional evolution equations with nonsmooth data: a concise overviewSolvability and approximation of two-side conservative fractional diffusion problems with variable-coefficient based on least-squaresAnalysis and discretization of a variable-order fractional wave equationMüntz Spectral Method for Two-Dimensional Space-Fractional Convection-Diffusion EquationDirect meshless local Petrov-Galerkin (DMLPG) method for time-fractional fourth-order reaction-diffusion problem on complex domainsFast finite difference methods for space-time fractional partial differential equations in three space dimensions with nonlocal boundary conditionsAnalysis of local discontinuous Galerkin method for time-space fractional convection-diffusion equationsSpectral approximation of a variable coefficient fractional diffusion equation in one space dimensionAn efficient collocation algorithm for multidimensional wave type equations with nonlocal conservation conditionsConvergence of a \(p\)-version/\(hp\)-version method for fractional differential equationsFractional Sturm-Liouville boundary value problems in unbounded domains: theory and applicationsEfficient spectral-Galerkin methods for fractional partial differential equations with variable coefficientsA new spectral method using nonstandard singular basis functions for time-fractional differential equationsAnalysis of spectral approximations using eigenfunctions of fractional Sturm-Liouville problemsEfficient second-order ADI difference schemes for three-dimensional Riesz space-fractional diffusion equationsApplication of fractional sub-equation method to nonlinear evolution equationsPreface: Numerical analysis of fractional differential equationsA unified difference-spectral method for time–space fractional diffusion equationsFractional-order uniaxial visco-elasto-plastic models for structural analysisA Petrov-Galerkin spectral element method for fractional elliptic problemsA high-order embedded domain method combining a predictor-corrector-Fourier-continuation-Gram method with an integral Fourier pseudospectral collocation method for solving linear partial differential equations in complex domainsAn exponentially convergent scheme in time for time fractional diffusion equations with non-smooth initial dataShifted fractional Jacobi spectral algorithm for solving distributed order time-fractional reaction-diffusion equationsJacobi spectral discretization for nonlinear fractional generalized seventh-order KdV equations with convergence analysisExtrapolating for attaining high precision solutions for fractional partial differential equationsAn efficient finite volume method for nonlinear distributed-order space-fractional diffusion equations in three space dimensionsA class of RBFs-based DQ methods for the space-fractional diffusion equations on 3D irregular domainsFractional Romanovski-Jacobi tau method for time-fractional partial differential equations with nonsmooth solutionsAn efficient space-time method for time fractional diffusion equationSpectral, tensor and domain decomposition methods for fractional PDEsTempered Fractional Sturm--Liouville EigenProblemsA Petrov--Galerkin Spectral Method of Linear Complexity for Fractional Multiterm ODEs on the Half LineFractional Pseudospectral Schemes with Equivalence for Fractional Differential EquationsNumerical methods for fractional partial differential equationsA numerical technique based on the shifted Legendre polynomials for solving the time-fractional coupled KdV equations


Uses Software


Cites Work


This page was built for publication: A unified Petrov-Galerkin spectral method for fractional PDEs