Chiang Mai Journal of Science

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A new parallel method for solving first order systems of ordinary differential equations using variable step size and order (back value) is developed.  The method, known as parallel R-point block method, calculates the numerical solution at more than one point simultaneously. The program of the method employed is run on a shared memory Sequent Symmetry S27 parallel computer. Computational advantages are presented comparing the results obtained by the new method with that of conventional 1-point method.  The numerical results show that the new method reduces the total number of steps and execution time.  It is also discovered that the accuracy of the parallel r-point block method and the 1-point method is comparable particularly when finer tolerances are used.

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