Exponential operator splitting time integration for spectral methods

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.