~Schemes for the solution of linear initial or boundary value problenm on a hypercube were developed by Katti and Neta [1] and tested and improved by Lustman, Neta and Katti [2]. Amov.g other procedures for parallel computers, fully implicit Runge-Kutta methods were discussed by Jackson and Norsett [3] and Lie [4]. Here, we develop a method based on extrapolation to the limit, which is useful even for nonlinear problesms. Numerical experiments show excellent accuracy when low order schemes are combined with polynomial extrapolation.

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In this paper there is developed and tested a parallel scheme for the solution of linear systems of ordinary initial value problems based on the box scheme and a modified recursive doubling technique. The box scheme may be replaced by any stable integrator. The algorithm can be modified to solve boundary value problems. Software for both problems is available upon request.

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