Chiang Mai Journal of Science

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Parallelism is the long-term answer to powerful computation. However, the design of parallel algorithms highly depends on the parallel computer architectures. Therefore, understanding the computer architecture is very crucial before any algorithm can be developed. In this paper, new parallel algorithms namely 2-point and 3-point explicit block methods for solving higher order ordinary differential equations (ODEs) directly are introduced. These methods compute the numerical solution at two and three points simultaneously and therefore exploit the advantages of a shared memory parallel computer architecture. Computational advantages are presented comparing the results obtained by the new methods with the conventional 1-point explicit method.

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