Abstract
<p>In this paper, utilizing Legendre polynomials as the basis functions in both space and time, we present a modified domain decomposition spectral method for 2-dimensional parabolic partial differential equations. For solving the obtained linear/nonlinear algebraic equations, a dimension expanding preconditioner is applied employing the obtained saddle construction of the coefficient matrix. Numerical examples are given to show the performance of the presented method and the efficiency of the preconditioner.</p>
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