Numerical Calculation of Bessel Functions by Solving Differential Equations and Its Application


IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E82-A   No.10   pp.2298-2301
Publication Date: 1999/10/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Numerical Analysis and Optimization
numerical method,  recurrence method,  Bessel function,  accuracy,  

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The method solving Bessel's differential equation for calculating numerical values of the Bessel function Jν(x) is not usually used, but it is made clear here that the differential equation method can give very precise numerical values of Jν(x), and is very effective if we do not mind computing time. Here we improved the differential equation method by using a new transformation of Jν(x). This letter also shows a method of evaluating the errors of Jν(x) calculated by this method. The recurrence method is used for calculating the Bessel function Jν(x) numerically. The convergence of the solutions in this method, however, is not yet examined for all of the values of the complex ν and the real x. By using the differential equation method, this letter will numerically ascertain the convergence of the solutions and the precision of Jν(x) calculated by the recurrence method.