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Runge-Kutta methods are applied to the numerical solution of hyperbolic partial differential equations. Conditions that they are locally stable are derived.

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Abstract. The objective of this paper is twofold :(a) To make it possible to perform matrix-vector operations in tensor product spaces, using only the factors (n-p1 words of information for ®"=1 A¡, A¡ £ £(£", E")) instead of the tensor-product operators themselves ((/>2)" words of information).(b) To produce efficient algorithms for solving systems of linear equations with coefficient matrices being tensor products of nonsingular matrices, with special application to the approximation of multidimensional linear functionals.