By William E. Ball, Robert I. Berns
Communications of the ACM,
August 1966,
Vol. 9 No. 8, Pages 626-633
10.1145/365758.365797
Comments
A procedure for numerically solving systems of ordinary differential equations is shown to also generate symbolic solutions. The procedure is based on a finite Taylor series expansion that includes an estimate of the error in the final result. A computer program is described that reads in a system of such equations and then generates the expansions for all of the dependent variables. The expansions are determined symbolically, hence any non-numeric parameters in the original equations are carried automatically into the final expansions. Thus the exact influence of any parameters on the problem solution can be easily displayed.
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