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Single and multi-interval Legendre $$\tau$$-methods in time for parabolic equations. (English) Zbl 1002.65111
Single and multi-interval spectral Legendre Petrov-Galerkin methods in time for the approximation of parabolic problems are considered. For the single interval spectral method in time, optimal error estimates in the $$L^2$$ norm are obtained. For the multi-interval spectral method in time, the $$L^2$$-optimal error estimate is valid in spatial. Numerical results show the efficiency of the method.

##### MSC:
 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs 35K05 Heat equation 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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