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. In this paper, we discuss the numerical solution, on a parallel computer, of a system of first order ordinary differential equations with initial data. Fully implicit Runge-Kutta methods were discussed by Jackson and Norsett (3) and Lie (4). Lie assumes that each processor of the parallel computer has vector capabilities. Katti and Neta (1) have developed schemes for the solution of linear initial value and boundary problems. These schemes were tested and improved by Lustman et al. (1). Here, we consider the solution of Initial Value Problems (linear or not), based on extrapolation to the limit. The system is solved independently by each processor, using different step sizes, then the results are combined by extrapolation to obtain higher accuracy. In the next section, we describe the ordinary differential equation solution schemes and the extrapolation procedure. Section 3 will detail the parallel algorithm. Numerical experiments are summarized in the last section. 2. ODE-INTEGRATION AND EXTRAPOLATION There are numerous schemes for the solution of first order IVPs:
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