|Author||Willers, I. M.|
|Source||ACM Digital Library|
|Publisher||Association for Computing Machinery (ACM)|
|Subject Keyword||Integration ♦ Singularities ♦ Program comparison ♦ Initial value problem ♦ Ordinary differential equations ♦ Taylor series ♦ Continued fractions|
|Abstract||A new integration algorithm is found, and an implementation is compared with other programmed algorithms. The new algorithm is a step-by-step procedure for solving the initial value problem in ordinary differential equations. It is designed to approximate poles of small integer order in the solutions of the differential equations by continued fractions obtained by manipulating the sums of truncated Taylor series expansions.The new method is compared with the Gragg-Bulirsch-Stoer, and the Taylor series method. The Taylor series method and the new method are shown to be superior in speed and accuracy, while the new method is shown to be most superior when the solution is required near a singularity. The new method can finally be seen to pass automatically through singularities where all the other methods which are discussed will have failed.|
|Description||Affiliation: CERN, Geneve, Switzerland (Willers, I. M.)|
|Age Range||18 to 22 years ♦ above 22 year|
|Education Level||UG and PG|
|Learning Resource Type||Article|
|Publisher Place||New York|
|Journal||Communications of the ACM (CACM)|
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