Legendre spectral collocation in space and time for PDEs

DOI10.1007/s00211-016-0834-xzbMath1365.65228OpenAlexW2522963784MaRDI QIDQ527815

Yong-Cai Geng, Sumit K. Garg

Publication date: 12 May 2017

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-016-0834-x

zbMATH Keywords

convergencenumerical examplesparallel computationLagrange spectral collocation method

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Initial-boundary value problems for second-order parabolic equations (35K20) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Parallel numerical computation (65Y05) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items

Efficient space-time Jacobi rational spectral methods for second order time-dependent problems on unbounded domains ⋮ Efficient space-time Legendre rational spectral method for parabolic problems in unbounded domains ⋮ Spectral collocation in space and time for linear PDEs ⋮ Space-time Legendre-Gauss-Lobatto collocation method for two-dimensional generalized sine-Gordon equation ⋮ Efficient space-time spectral methods for second-order problems on unbounded domains ⋮ Space-time spectral method for the Stokes problem ⋮ Space–time spectral collocation method for one-dimensional PDE constrained optimisation ⋮ Legendre-Gauss-Radau Spectral Collocation Method for Nonlinear Second-Order Initial Value Problems with Applications To Wave Equations ⋮ Spectral methods in space and time for parabolic problems on semi-infinite domains ⋮ Stabilized enhancement for large time computation using exponential spectral process method ⋮ Chebyshev spectral collocation in space and time for the heat equation ⋮ Legendre-tau-Galerkin and spectral collocation method for nonlinear evolution equations ⋮ A class of compact boundary value methods applied to semi-linear reaction-diffusion equations

Uses Software

• Matlab

Cites Work

• Unnamed Item
• Unnamed Item
• A Legendre spectral method in time for first-order hyperbolic equations
• Fourierization of the Legendre-Galerkin method and a new space-time spectral method
• Legendre-Gauss collocation methods for ordinary differential equations
• Spectral elements for transport-dominated equations
• Convergence of spectral method in time for Burgers' equation
• Spectral deferred correction methods for ordinary differential equations
• Single and multi-interval Legendre \(\tau\)-methods in time for parabolic equations
• Legendre spectral collocation method for second-order nonlinear ordinary/partial differential equations
• Analysis of Hamiltonian boundary value methods (HBVMs): A class of energy-preserving Runge-Kutta methods for the numerical solution of polynomial Hamiltonian systems
• Spectral methods on arbitrary grids
• A Well-Conditioned Collocation Method Using a Pseudospectral Integration Matrix
• Legendre–Gauss-type spectral collocation algorithms for nonlinear ordinary/partial differential equations
• Spectral Methods
• A Simple Proposal for Parallel Computation Over Time of an Evolutionary Process with Implicit Time Stepping
• Spectral Methods for Time-Dependent Problems
• Spectral Methods in Time for Parabolic Problems
• A Hessenberg-Schur method for the problem AX + XB= C
• Spectral Methods and Their Applications
• Spectral Methods in MATLAB
• Spectral Methods in Time for Hyperbolic Equations
• A Space-Time Multigrid Method for Parabolic Partial Differential Equations
• A Practical Guide to Pseudospectral Methods
• A Parallel Space-Time Algorithm
• On exponential convergence of Gegenbauer interpolation and spectral differentiation
• Stable Parareal in Time Method for First- and Second-Order Hyperbolic Systems
• Parallel Time Integration with Multigrid
• Space‐time spectral collocation method for the one‐dimensional sine‐<scp>G</scp>ordon equation
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• Numerical Analysis of Partial Differential Equations
• Analysis of the Parareal Time‐Parallel Time‐Integration Method
• Spectral Methods
• Galerkin-Chebyshev spectral method and block boundary value methods for two-dimensional semilinear parabolic equations

This page was built for publication: Legendre spectral collocation in space and time for PDEs