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The method solving Bessel's differential equation for calculating numerical values of the Bessel function *J*_{ν}(*x*) is not usually used, but it is made clear here that the differential equation method can give very precise numerical values of *J*_{ν}(*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 *J*_{ν}(*x*). This letter also shows a method of evaluating the errors of *J*_{ν}(*x*) calculated by this method. The recurrence method is used for calculating the Bessel function *J*_{ν}(*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 *J*_{ν}(*x*) calculated by the recurrence method.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E82-A No.10 pp.2298-2301

- Publication Date
- 1999/10/25

- Publicized

- Online ISSN

- DOI

- Type of Manuscript
- LETTER

- Category
- Numerical Analysis and Optimization

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Mohd ABDUR RASHID, Masao KODAMA, "Numerical Calculation of Bessel Functions by Solving Differential Equations and Its Application" in IEICE TRANSACTIONS on Fundamentals,
vol. E82-A, no. 10, pp. 2298-2301, October 1999, doi: .

Abstract: The method solving Bessel's differential equation for calculating numerical values of the Bessel function *J*_{ν}(*x*) is not usually used, but it is made clear here that the differential equation method can give very precise numerical values of *J*_{ν}(*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 *J*_{ν}(*x*). This letter also shows a method of evaluating the errors of *J*_{ν}(*x*) calculated by this method. The recurrence method is used for calculating the Bessel function *J*_{ν}(*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 *J*_{ν}(*x*) calculated by the recurrence method.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e82-a_10_2298/_p

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@ARTICLE{e82-a_10_2298,

author={Mohd ABDUR RASHID, Masao KODAMA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Numerical Calculation of Bessel Functions by Solving Differential Equations and Its Application},

year={1999},

volume={E82-A},

number={10},

pages={2298-2301},

abstract={The method solving Bessel's differential equation for calculating numerical values of the Bessel function *J*_{ν}(*x*) is not usually used, but it is made clear here that the differential equation method can give very precise numerical values of *J*_{ν}(*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 *J*_{ν}(*x*). This letter also shows a method of evaluating the errors of *J*_{ν}(*x*) calculated by this method. The recurrence method is used for calculating the Bessel function *J*_{ν}(*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 *J*_{ν}(*x*) calculated by the recurrence method.},

keywords={},

doi={},

ISSN={},

month={October},}

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TY - JOUR

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

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 2298

EP - 2301

AU - Mohd ABDUR RASHID

AU - Masao KODAMA

PY - 1999

DO -

JO - IEICE TRANSACTIONS on Fundamentals

SN -

VL - E82-A

IS - 10

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - October 1999

AB - The method solving Bessel's differential equation for calculating numerical values of the Bessel function *J*_{ν}(*x*) is not usually used, but it is made clear here that the differential equation method can give very precise numerical values of *J*_{ν}(*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 *J*_{ν}(*x*). This letter also shows a method of evaluating the errors of *J*_{ν}(*x*) calculated by this method. The recurrence method is used for calculating the Bessel function *J*_{ν}(*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 *J*_{ν}(*x*) calculated by the recurrence method.

ER -