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We devise a class of fast wavelet based algorithms for linear evolution equations whose coefficients are time independent. The method draws on the work of Beylkin, Coifman, and Rokhlin 1 which they applied to general Calderon-Zygmund type integral operators. We apply a modification of their idea to linear hyperbolic and parabolic equations, with spatially varying coefficients. A significant speedup over standard methods is obtained when applied to hyperbolic equations in one space dimension and parabolic equations in multidimensions. wavelets; hyperbolic; parabolic; numerical methods.

A class was devised of fast wavelet based algorithms for linear evolution equations whose coefficients are time independent. The method draws on the work of Beylkin, Coifman, and Rokhlin which they applied to general Calderon-Zygmund type integral operators. A modification of their idea is applied to linear hyperbolic and parabolic equations, with spatially varying coefficients. A significant speedup over standard methods is obtained when applied to hyperbolic equations in one space dimension and parabolic equations in multidimensions.