Exponential operator splitting time integration for spectral methods

Authors:
Roman Kozlov
Affiliations:
Department of Mathematics, University of Bergen, Jonannes Brunsgate 12, 5008 Bergen, Norway
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 5
Cited 1

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Higher-order operator splitting methods for deterministic parabolic equations

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Exponential splitting time integration for pseudospectral methods on moving meshes

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Abstract

Pseudospectral spatial discretization by orthogonal polynomials and Strang splitting method for time integration are applied to second-order linear evolutionary PDEs. Before such a numerical integration can be used the original PDE is transformed into a suitable form. Trigonometric, Jacobi (and some of their special cases), generalized Laguerre and Hermite polynomials are considered. A double representation of a function (by coefficients of a polynomial expansion and by values at the nodes associated with a suitable quadrature formula) is used for numerical implementation so that it is possible to avoid calculations of matrix exponentials.