Spectral methods in time for a class of parabolic partial differential equations

DOI10.1016/S0021-9991(05)80008-7zbMath0758.65064MaRDI QIDQ1195120

Brian J. Spencer, Rodney A. Worthing, Glenn R. Ierley

Publication date: 12 October 1992

Published in: Journal of Computational Physics (Search for Journal in Brave)

zbMATH Keywords

Fourier expansionnonlinear parabolic equationsspectral methodsChebyshev expansion

Mathematics Subject Classification ID

Related Items (26)

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 spectral method for a weakly singular parabolic partial integro-differential equation on irregular domains ⋮ A Legendre spectral method in time for first-order hyperbolic equations ⋮ Axisymmetric fully spectral code for hyperbolic equations ⋮ Spectral method in time for KdV equations ⋮ Legendre–Gauss-type spectral collocation algorithms for nonlinear ordinary/partial differential equations ⋮ Fully spectral collocation method for nonlinear parabolic partial integro-differential equations ⋮ Efficient space-time spectral methods for second-order problems on unbounded domains ⋮ Convergence of spectral method in time for Burgers' equation ⋮ A space-time pseudospectral method for solving multi-dimensional quasi-linear parabolic partial differential (Burgers') equations ⋮ A spectrally accurate time ‐ space pseudospectral method for viscous Burgers' equation ⋮ Space-time spectral method for the Stokes problem ⋮ Spectral methods in space and time for parabolic problems on semi-infinite domains ⋮ Numerical solution for the linear time and space fractional diffusion equation ⋮ Chebyshev spectral collocation in space and time for the heat equation ⋮ Legendre spectral collocation method for second-order nonlinear ordinary/partial differential equations ⋮ New space-time spectral and structured spectral element methods for high order problems ⋮ Numerical solution of nonlinear Schrödinger equation by using time-space pseudo-spectral method ⋮ Jacobi-Gauss-Lobatto collocation method for solving nonlinear reaction-diffusion equations subject to Dirichlet boundary conditions ⋮ Spectral methods for numerical relativity ⋮ A Jacobi collocation method for solving nonlinear Burgers-type equations ⋮ A spectrally accurate time-space pseudospectral method for reaction-diffusion malaria infection model ⋮ Legendre-Gauss-Lobatto spectral collocation method for nonlinear delay differential equations ⋮ Block-marching in time with DQ discretization: An efficient method for time-dependent problems

Cites Work

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• A spectral element method for fluid dynamics: Laminar flow in a channel expansion
• Spectral and finite difference solutions of the Burgers equations
• Order and complexity in the Kuramoto-Sivashinsky model of weakly turbulent interfaces
• The accurate solution of Poisson's equation by expansion in Chebyshev polynomials
• Chaotic behaviour of soliton lattice in an unstable dissipative- dispersive nonlinear system
• Symplectic integration of Hamiltonian systems
• Spectral Methods in Time for Hyperbolic Equations
• Long Waves on Liquid Films

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